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KUMMER SUM

  • Kummer sum
  • Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who

    Kummer sum

    Kummer_sum

  • Gauss sum
  • Sum in algebraic number theory

    calculate certain zeta functions. Quadratic Gauss sum Elliptic Gauss sum Jacobi sum Kummer sum Kloosterman sum Gaussian period Hasse–Davenport relation Chowla–Mordell

    Gauss sum

    Gauss_sum

  • Ernst Kummer
  • German mathematician (1810–1893)

    divisors of binomial coefficients Kummer's function Kummer sum Kummer variety Kummer–Vandiver conjecture Kummer's transformation of series Ideal number

    Ernst Kummer

    Ernst Kummer

    Ernst_Kummer

  • Quadratic Gauss sum
  • Sum type in number theory

    2 and an odd prime number p, and for k ≥ 4 and p = 2. Gauss sum Gaussian period Kummer sum Landsberg–Schaar relation M. Murty, S. Pathak, The Mathematics

    Quadratic Gauss sum

    Quadratic_Gauss_sum

  • Series (mathematics)
  • Infinite sum

    (1852), Chebyshev (1852), and Arndt (1853). General criteria began with Kummer (1835), and have been studied by Eisenstein (1847), Weierstrass in his various

    Series (mathematics)

    Series_(mathematics)

  • Confluent hypergeometric function
  • Solution of a confluent hypergeometric equation

    hypergeometric functions: Kummer's (confluent hypergeometric) function M(a, b, z), introduced by Kummer (1837), is a solution to Kummer's differential equation

    Confluent hypergeometric function

    Confluent hypergeometric function

    Confluent_hypergeometric_function

  • Kummer's theorem
  • Describes the highest power of primes dividing a binomial coefficient

    In mathematics, Kummer's theorem is a formula for the exponent of the highest power of a prime number p that divides a given binomial coefficient. In other

    Kummer's theorem

    Kummer's_theorem

  • Kummer theory
  • Theory in abstract algebra

    In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of nth roots

    Kummer theory

    Kummer_theory

  • Kummer's transformation of series
  • Mathematical method

    first suggested by Ernst Kummer in 1837. Let A = ∑ n = 1 ∞ a n {\displaystyle A=\sum _{n=1}^{\infty }a_{n}} be an infinite sum whose value we wish to compute

    Kummer's transformation of series

    Kummer's_transformation_of_series

  • Ratio test
  • Criterion for the convergence of a series

    sum _{j=1}^{K}\prod _{k=1}^{j}\ln _{(K-k+1)}(n)-1+o(1)} . Hence, ρ Kummer = ρ Extended Bertrand − 1 {\displaystyle \rho _{\text{Kummer}}=\rho _{\text{Extended

    Ratio test

    Ratio_test

  • Dedekind–Kummer theorem
  • Theorem in algebraic number theory

    In algebraic number theory, the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. It

    Dedekind–Kummer theorem

    Dedekind–Kummer_theorem

  • Kummer's conjecture
  • Topics referred to by the same term

    Kummer–Vandiver conjecture about class numbers of cyclotomic fields Kummer's conjecture about the Kummer sum This disambiguation page lists mathematics articles associated

    Kummer's conjecture

    Kummer's_conjecture

  • Kummer's function
  • Mathematical function

    there are several functions known as Kummer's function. One is known as the confluent hypergeometric function of Kummer. Another one, defined below, is related

    Kummer's function

    Kummer's_function

  • Fermat's Last Theorem
  • 17th-century conjecture proved by Andrew Wiles in 1994

    Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Building on Kummer's work

    Fermat's Last Theorem

    Fermat's Last Theorem

    Fermat's_Last_Theorem

  • Vaughan's identity
  • Identity in analytic number theory

    to simplify the proof of the Bombieri–Vinogradov theorem and to study Kummer sums (see the references and external links below). In Chapter 25 of Davenport

    Vaughan's identity

    Vaughan's_identity

  • Samuel James Patterson
  • British mathematician

    exponential sums in analytical number theory. In 1978, together with Roger Heath-Brown, he disproved the Kummer conjecture on cubic Gauss sums. He proposed

    Samuel James Patterson

    Samuel James Patterson

    Samuel_James_Patterson

  • Perimeter of an ellipse
  • {\displaystyle h=(a-b)^{2}/(a+b)^{2}} . Found by James Ivory, Bessel and Kummer, there are several equivalent ways to write it. The most concise is in terms

    Perimeter of an ellipse

    Perimeter of an ellipse

    Perimeter_of_an_ellipse

  • Generalized hypergeometric function
  • Family of power series in mathematics

    {x^{i}}{i!}},\end{aligned}}} which is a finite sum if b-d is a non-negative integer. Kummer's relation is 2 F 1 ( 2 a , 2 b ; a + b + 1 2 ; x ) =

    Generalized hypergeometric function

    Generalized hypergeometric function

    Generalized_hypergeometric_function

  • Hypergeometric function
  • Function defined by a hypergeometric series

    Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857)

    Hypergeometric function

    Hypergeometric function

    Hypergeometric_function

  • Fermat's theorem on sums of two squares
  • Condition under which an odd prime is a sum of two squares

    In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}

    Fermat's theorem on sums of two squares

    Fermat's_theorem_on_sums_of_two_squares

  • 209 (number)
  • Natural number

    prime factors of any Kummer number must be distinct from the primes in its product formula as a Kummer number. However, the Kummer numbers are not all

    209 (number)

    209_(number)

  • Regular prime
  • Type of prime number

    theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes

    Regular prime

    Regular_prime

  • Bernoulli number
  • Rational number sequence

    number Genocchi number Kummer's congruences Poly-Bernoulli number Hurwitz zeta function Euler summation Stirling polynomial Sums of powers Translation

    Bernoulli number

    Bernoulli_number

  • Prime number
  • Number divisible only by 1 and itself

    electronic computers. For instance, Beiler writes that number theorist Ernst Kummer loved his ideal numbers, closely related to the primes, "because they had

    Prime number

    Prime number

    Prime_number

  • Witt vector
  • Mathematical concept named for Ernst Witt

    Ernst Eduard Kummer studied cyclic extensions of fields as part of his work on Fermat's Last Theorem. This led to the subject known as Kummer theory. Let

    Witt vector

    Witt_vector

  • Convergence tests
  • Mathematical criterion about whether a series converges

    convergence or divergence of an infinite series ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} . If the limit of the summand is undefined or nonzero

    Convergence tests

    Convergence_tests

  • Euler's constant
  • Difference between logarithm and harmonic series

    _{k=1}^{3\cdot 2}{\frac {k}{k+3^{2}}}+\cdots \end{aligned}}} From the Malmsten–Kummer expansion for the logarithm of the gamma function we get: γ = log ⁡ π −

    Euler's constant

    Euler's constant

    Euler's_constant

  • Multinomial theorem
  • Generalization of the binomial theorem to other polynomials

    multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from

    Multinomial theorem

    Multinomial_theorem

  • Binomial coefficient
  • Number of subsets of a given size

    . {\displaystyle \sum _{n=0}^{\infty }\sum _{k=0}^{\infty }{\binom {n+k}{k}}{\frac {x^{k}y^{n}}{(n+k)!}}=e^{x+y}.} In 1852, Kummer proved that if m and

    Binomial coefficient

    Binomial coefficient

    Binomial_coefficient

  • Stickelberger's theorem
  • Gives information about the Galois module structure of class groups of cyclotomic fields

    class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the general result is due to Ludwig Stickelberger (1890). Let

    Stickelberger's theorem

    Stickelberger's_theorem

  • Euclid number
  • Product of prime numbers, plus one

    infinitely many prime numbers. A Euclid number of the second kind (also called Kummer number) is an integer of the form En = pn # − 1, where pn # is the nth primorial

    Euclid number

    Euclid_number

  • Herbrand–Ribet theorem
  • Result on the class group of certain number fields, strengthening Ernst Kummer's theorem

    the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the

    Herbrand–Ribet theorem

    Herbrand–Ribet_theorem

  • Ideal (ring theory)
  • Submodule of a mathematical ring

    the usual ideals are sometimes called integral ideals for clarity. Ernst Kummer invented the concept of ideal numbers to serve as the "missing" factors

    Ideal (ring theory)

    Ideal_(ring_theory)

  • K3 surface
  • Type of smooth complex surface of kodaira dimension 0

    s'agit des variétés kählériennes dites K3, ainsi nommées en l'honneur de Kummer, Kähler, Kodaira et de la belle montagne K2 au Cachemire. In the second

    K3 surface

    K3 surface

    K3_surface

  • Law of small numbers
  • Topics referred to by the same term

    that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss sums The strong law of small numbers, an observation made by

    Law of small numbers

    Law_of_small_numbers

  • Velopharyngeal insufficiency
  • Failure of the soft palate to prevent airflow through the nose during speech

    Seminars in Speech and Language, 32(2), 191-199. Kummer AW. (2020). Kummer AW. (2020). Speech Therapy. In Kummer, AW. Cleft Palate and Craniofacial Conditions:

    Velopharyngeal insufficiency

    Velopharyngeal_insufficiency

  • Algebraic number theory
  • Branch of number theory

    of Emmy Noether. Ideals generalize Ernst Eduard Kummer's ideal numbers, devised as part of Kummer's 1843 attempt to prove Fermat's Last Theorem. David

    Algebraic number theory

    Algebraic number theory

    Algebraic_number_theory

  • P-adic number
  • Number system extending the rational numbers

    described by Kurt Hensel in 1897, though, with hindsight, some of Ernst Kummer's earlier work can be interpreted as implicitly using p-adic numbers. Roughly

    P-adic number

    P-adic number

    P-adic_number

  • Lucas's theorem
  • Number theory theorem

    2017-02-02. Désarménien, Jacques (March 1982). "Un Analogue des Congruences de Kummer pour les q-nombres d'Euler". European Journal of Combinatorics. 3 (1): 19–28

    Lucas's theorem

    Lucas's_theorem

  • Gamma function
  • Extension of the factorial function

    z)+{\frac {1}{\pi }}\sum _{n=1}^{\infty }{\frac {\log n}{n}}\sin(2\pi nz),} which was for a long time attributed to Ernst Kummer, who derived it in 1847

    Gamma function

    Gamma function

    Gamma_function

  • Incomplete gamma function
  • Types of special mathematical functions

    {\displaystyle \gamma (s,z)=\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{k!}}{\frac {z^{s+k}}{s+k}}={\frac {z^{s}}{s}}M(s,s+1,-z),} where M is Kummer's confluent hypergeometric

    Incomplete gamma function

    Incomplete gamma function

    Incomplete_gamma_function

  • Greatest common divisor
  • Largest integer that divides given integers

    even when there is no greatest common divisor of a and b. (Indeed, Ernst Kummer used this ideal as a replacement for a GCD in his treatment of Fermat's

    Greatest common divisor

    Greatest_common_divisor

  • Dedekind domain
  • Algebra with unique prime factorization

    ring Z [ ζ n ] {\displaystyle \mathbb {Z} [\zeta _{n}]} is a UFD. Ernst Kummer had shown three years before that this was not the case already for n =

    Dedekind domain

    Dedekind_domain

  • Hermite polynomials
  • Polynomial sequence

    {3}{2}};x^{2}{\big )},\end{aligned}}} where 1F1(a, b; z) = M(a, b; z) is Kummer's confluent hypergeometric function. H e 2 n ( x ) = ( − 1 ) n ( 2 n − 1

    Hermite polynomials

    Hermite_polynomials

  • List of unsolved problems in mathematics
  • extensions of Q {\displaystyle \mathbb {Q} } to any base number field. Kummer–Vandiver conjecture: primes p {\displaystyle p} do not divide the class

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Discrete Chebyshev polynomials
  • Type of discrete orthogonal polynomials

    K. Pearce; L. Reichel; K.C. Richards (1998). "Gram Polynomials and the Kummer Function". Journal of Approximation Theory. 94: 128–143. doi:10.1006/jath

    Discrete Chebyshev polynomials

    Discrete_Chebyshev_polynomials

  • 0
  • Number

    be found by another method, such as l'Hôpital's rule. The sum of 0 numbers (the empty sum) is 0, and the product of 0 numbers (the empty product) is

    0

    0

  • Legendre's formula
  • Number theory expression

    {1}{p-1}}\left(n-s_{p}(n)\right).\end{aligned}}} Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive

    Legendre's formula

    Legendre's_formula

  • Multiplication theorem
  • Identity obeyed by many special functions related to the gamma function

    periodic zeta function, taking z = log q. The duplication formula for Kummer's function is 2 1 − n Λ n ( − z 2 ) = Λ n ( z ) + Λ n ( − z ) {\displaystyle

    Multiplication theorem

    Multiplication_theorem

  • Error function
  • Sigmoid shape special function

    denominator terms form sequence A007680 in the OEIS. This is a special case of Kummer's function: erf ⁡ ( z ) = 2 z π 1 F 1 ( 1 2 , 3 2 , − z 2 ) . {\displaystyle

    Error function

    Error function

    Error_function

  • Mechanical Turk
  • Chess-playing automaton hoax (1770–1854)

    1859, a letter published in the Philadelphia Sunday Dispatch by William F. Kummer, who worked as an operator under John Mitchell, revealed how a candle inside

    Mechanical Turk

    Mechanical Turk

    Mechanical_Turk

  • Beta distribution
  • Probability distribution

    density function. The characteristic function of the beta distribution is Kummer's confluent hypergeometric function (of the first kind): φ X ( α ; β ; t

    Beta distribution

    Beta distribution

    Beta_distribution

  • Factorial
  • Product of numbers from 1 to n

    Legendre's formula to the product formula for binomial coefficients produces Kummer's theorem, a similar result on the exponent of each prime in the factorization

    Factorial

    Factorial

  • List of mathematical functions
  • form of the polylogarithm. Dilogarithm Incomplete Fermi–Dirac integral Kummer's function Riesz function Hypergeometric functions: Versatile family of power

    List of mathematical functions

    List_of_mathematical_functions

  • Sun cross
  • Circle containing four or more spokes

    herz des Weltkrieges: General Ludendorffs Wertung als Deutscher, Georg Kummer, 1935, p. 244. entry at the Nebra sky disk exhibition site

    Sun cross

    Sun cross

    Sun_cross

  • Arf invariant
  • Invariant of a quadratic form over a field of characteristic 2

    discriminant takes values in F*/(F*)2, which can be identified with H1(F, F2) by Kummer theory. If the field K is perfect, then every nonsingular quadratic form

    Arf invariant

    Arf invariant

    Arf_invariant

  • Laguerre polynomials
  • Sequence of differential equation solutions

    Laguerre functions are defined by confluent hypergeometric functions and Kummer's transformation as L n ( α ) ( x ) := ( n + α n ) M ( − n , α + 1 , x )

    Laguerre polynomials

    Laguerre polynomials

    Laguerre_polynomials

  • P-adic L-function
  • interpolation of special values of L-functions. For example, Kubota–Leopoldt used Kummer's congruences for Bernoulli numbers to construct a p-adic L-function, the

    P-adic L-function

    P-adic_L-function

  • Weil pairing
  • Binary function non degenerative defined between the point of twist of an abelian variety

    unity w ( P , Q ) ∈ μ n {\displaystyle w(P,Q)\in \mu _{n}} by means of Kummer theory, for any two points P , Q ∈ E ( K ) [ n ] {\displaystyle P,Q\in E(K)[n]}

    Weil pairing

    Weil_pairing

  • Clausen function
  • Transcendental single-variable function

    \operatorname {Cl} _{2}(\theta )={\mathcal {L}}s_{2}^{0}(\theta )} Ernst Kummer and Rogers give the relation Li 2 ⁡ ( e i θ ) = ζ ( 2 ) − θ ( 2 π − θ )

    Clausen function

    Clausen function

    Clausen_function

  • Polylogarithm
  • Special mathematical function

    _{s}(-z)+\operatorname {Li} _{s}(z)=2^{1-s}\operatorname {Li} _{s}(z^{2}).} Kummer's function obeys a very similar duplication formula. This is a special case

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Abstract algebra
  • Branch of mathematics

    were UFDs, yet as Kummer pointed out, Q ( ζ 23 ) ) {\displaystyle \mathbb {Q} (\zeta _{23}))} was not a UFD. In 1846 and 1847 Kummer introduced ideal numbers

    Abstract algebra

    Abstract algebra

    Abstract_algebra

  • Sum activity of peripheral deiodinases
  • Medical diagnostic method

    The sum activity of peripheral deiodinases (GD, also referred to as deiodination capacity, total deiodinase activity or, if calculated from levels of

    Sum activity of peripheral deiodinases

    Sum_activity_of_peripheral_deiodinases

  • Equations defining abelian varieties
  • small values of d > 1. The interest in nineteenth century geometry in the Kummer surface came in part from the way a quartic surface represented a quotient

    Equations defining abelian varieties

    Equations_defining_abelian_varieties

  • Class number formula
  • Formula in number theory

    considered. In that case there is a further formulation possible, as shown by Kummer. The regulator, a calculation of volume in 'logarithmic space' as divided

    Class number formula

    Class_number_formula

  • Euclidean algorithm
  • Algorithm for computing greatest common divisors

    This failure of unique factorization in some cyclotomic fields led Ernst Kummer to the concept of ideal numbers and, later, Richard Dedekind to ideals.

    Euclidean algorithm

    Euclidean algorithm

    Euclidean_algorithm

  • Navier–Stokes equations
  • Equations of motion for viscous fluids

    Navier–Stokes equations in Cartesian coordinate can be given with the help of the Kummer's functions with quadratic arguments. For the compressible Navier–Stokes

    Navier–Stokes equations

    Navier–Stokes_equations

  • Mixed radix
  • Type of numeral systems

    theory II, Kluwer Academic Publishers, 2004, Chapter 4, pp. 384-386. E. E. Kummer, Neuer elementarer Beweis des Satzes, dass die Anzahl aller Primzahlen eine

    Mixed radix

    Mixed_radix

  • Fresnel integral
  • Special function defined by an integral

    analytical extension to the whole plane less where lie the poles of Γ(a−1). The Kummer transformation of the confluent hypergeometric function is ∫ x m e i x n

    Fresnel integral

    Fresnel integral

    Fresnel_integral

  • Frobenius method
  • Method for solving ordinary differential equations

    C must be zero. Example: consider the following differential equation (Kummer's equation with a = 1 and b = 2): z u ″ + ( 2 − z ) u ′ − u = 0 {\displaystyle

    Frobenius method

    Frobenius method

    Frobenius_method

  • Fundamental theorem of arithmetic
  • Integers have unique prime factorizations

    or over a field, Euclidean domains and principal ideal domains. In 1843 Kummer introduced the concept of ideal number, which was developed further by Dedekind

    Fundamental theorem of arithmetic

    Fundamental theorem of arithmetic

    Fundamental_theorem_of_arithmetic

  • List of abstract algebra topics
  • Branch of mathematics that studies algebraic structures

    field Real closed field Galois theory Galois group Inverse Galois problem Kummer theory Module (mathematics) Bimodule Annihilator (ring theory) Submodule

    List of abstract algebra topics

    List_of_abstract_algebra_topics

  • Number
  • Used to count, measure, and label

    = 0 for higher values of k. This generalization is largely due to Ernst Kummer, who also invented ideal numbers, which were expressed as geometrical entities

    Number

    Number

    Number

  • Dixon's identity
  • On finite sums of products of three binomial coefficients, and a hypergeometric sum

    This holds for Re(1 + 1⁄2a − b − c) > 0. As c tends to −∞ it reduces to Kummer's formula for the hypergeometric function 2F1 at −1. Dixon's theorem can

    Dixon's identity

    Dixon's_identity

  • Cyclic group
  • Mathematical group that can be generated as the set of powers of a single element

    For fields of characteristic zero, such extensions are the subject of Kummer theory, and are intimately related to solvability by radicals. For an extension

    Cyclic group

    Cyclic group

    Cyclic_group

  • Gotthold Eisenstein
  • German mathematician (1823–1852)

    Eisenstein sum Eisenstein series Eisenstein's theorem Eisenstein triple Eisenstein–Kronecker number Real analytic Eisenstein series Elliptic Gauss sum "Eisenstein

    Gotthold Eisenstein

    Gotthold Eisenstein

    Gotthold_Eisenstein

  • Berliner FC Dynamo
  • German association football club

    Hamburg: Norddeutscher Rundfunk. 4 October 2018. Retrieved 6 October 2025. Kummer, Micharl (2010). Die Fußballclubs Rot-Weiß Erfurt und Carl Zeiss Jena und

    Berliner FC Dynamo

    Berliner FC Dynamo

    Berliner_FC_Dynamo

  • Disquisitiones Arithmeticae
  • 1798 textbook by Carl Friedrich Gauss

    starting point for other 19th-century European mathematicians, including Ernst Kummer, Peter Gustav Lejeune Dirichlet and Richard Dedekind. Many of Gauss's annotations

    Disquisitiones Arithmeticae

    Disquisitiones Arithmeticae

    Disquisitiones_Arithmeticae

  • Von Staudt–Clausen theorem
  • Determines the fractional part of Bernoulli numbers

    n 1 p , {\displaystyle B_{2n}=I_{n}-\sum _{(p-1)|2n}{\frac {1}{p}},} where In is an integer, as desired. Kummer's congruence H. Rademacher, Analytic Number

    Von Staudt–Clausen theorem

    Von_Staudt–Clausen_theorem

  • Exponential integral
  • Special function defined by an integral

    H n {\displaystyle \mathrm {Ein} (z)=e^{-z}\,\sum _{n=1}^{\infty }{\frac {z^{n}}{n!}}H_{n}} Kummer's equation z d 2 w d z 2 + ( b − z ) d w d z − a w

    Exponential integral

    Exponential integral

    Exponential_integral

  • Love & Fear
  • 2025 studio album by Zac Brown Band

    violin (6) Neil Konouchi – tuba (6) Annaliese Kowert – violin (6) Jennifer Kummer – French horn (6) Betsy Lamb – viola (6) Rachel Miller – harp (6) Craig

    Love & Fear

    Love_&_Fear

  • Ellipse
  • Plane curve

    surrounding two focal points, such that for all points on the curve, the sum of both distances to the two focal points is a constant. It generalizes a

    Ellipse

    Ellipse

    Ellipse

  • Belmont Stakes
  • American stakes race for Thoroughbreds, part of the Triple Crown

    Herbert J. Thompson Edward R. Bradley Sloppy 2:32.80 1928 Vito Clarence Kummer Max Hirsch Alfred H. Cosden Fast 2:33.20 1927 Chance Shot Earl Sande Pete

    Belmont Stakes

    Belmont Stakes

    Belmont_Stakes

  • Block design
  • Structure in combinatorial mathematics

    biplanes of order 4 (and 16 points, lines of size 6; a 2-(16,6,2)). One is the Kummer configuration. These three designs are also Menon designs. There are four

    Block design

    Block_design

  • Riesz function
  • Mathematical function

    = x exp ⁡ ( − x ) . {\displaystyle \ {\sum _{n=1}^{\infty }{\rm {Riesz}}(x/n^{2})=x\exp(-x)}.} Using Kummer's method for accelerating convergence gives

    Riesz function

    Riesz function

    Riesz_function

  • Thyroid function tests
  • Collective term for blood tests used to check the function of the thyroid

    El-Battrawy, I; Akin, I; Borggrefe, M; Mügge, A; Patsalis, PC; Urban, A; Kummer, M; Vasileva, S; Stachon, A; Hering, S; Dietrich, JW (12 November 2020)

    Thyroid function tests

    Thyroid_function_tests

  • Series acceleration
  • Mathematical technique for improving convergence

    techniques for series acceleration are Euler's transformation of series and Kummer's transformation of series. A variety of much more rapidly convergent and

    Series acceleration

    Series_acceleration

  • List of conjectures
  • hypothesis (not a conjecture to start with) Doomsday conjecture Euler's sum of powers conjecture Ganea conjecture Generalized Smith conjecture Hauptvermutung

    List of conjectures

    List_of_conjectures

  • Number theory
  • Branch of pure mathematics

    integers.) The initial impetus for the development of ideal numbers (by Kummer) seems to have come from the study of higher reciprocity laws, that is,

    Number theory

    Number theory

    Number_theory

  • Chi distribution
  • Probability distribution

    {t^{2}}{2}}\right),} where M ( a , b , z ) {\displaystyle M(a,b,z)} is Kummer's confluent hypergeometric function. The characteristic function is given

    Chi distribution

    Chi distribution

    Chi_distribution

  • Kapteyn series
  • Jankov Maširević, Dragana; Pogány, Tibor K. (2017). "Series of Bessel and Kummer-Type Functions". Lecture Notes in Mathematics. Cham: Springer International

    Kapteyn series

    Kapteyn_series

  • Lemniscate elliptic functions
  • Mathematical functions

    Katz, Nicholas M. (1975). "The congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz numbers". Mathematische Annalen. 216 (1): 1–4. doi:10

    Lemniscate elliptic functions

    Lemniscate elliptic functions

    Lemniscate_elliptic_functions

  • Prime ideal
  • Ideal in a ring which has properties similar to prime elements

    not countably generated is prime. Radical ideal Maximal ideal Dedekind–Kummer theorem Residue field Dummit, David S.; Foote, Richard M. (2004). Abstract

    Prime ideal

    Prime ideal

    Prime_ideal

  • Roger Heath-Brown
  • British mathematician

    1978 he proved the Kummer conjecture on cubic Gauss sums in its equidistribution form. He has applied Burgess's method on character sums to the ranks of

    Roger Heath-Brown

    Roger Heath-Brown

    Roger_Heath-Brown

  • Étale cohomology
  • Sheaf cohomology on the étale site

    _{m})\to H^{2}(X,\mathbf {G} _{m})\to \\&\to \cdots \end{aligned}}} of the Kummer exact sequence of étale sheaves 1 → μ n → G m → ( ⋅ ) n G m → 1. {\displaystyle

    Étale cohomology

    Étale_cohomology

  • Superelliptic curve
  • corresponding function field extension) is cyclic. The fundamental theorem of Kummer theory implies [citation needed] that a superelliptic curve of degree m

    Superelliptic curve

    Superelliptic_curve

  • Geometrical optics
  • Model of optics describing light as geometric rays

    "Discussion of the general form for light waves" E. Kummer, "General theory of rectilinear ray systems" E. Kummer, presentation on optically-realizable rectilinear

    Geometrical optics

    Geometrical_optics

  • Field (mathematics)
  • Algebraic structure with addition, multiplication, and division

    satisfies ζn = 1 and ζm ≠ 1 for all 0 < m < n. For n being a regular prime, Kummer used cyclotomic fields to prove Fermat's Last Theorem, which asserts the

    Field (mathematics)

    Field (mathematics)

    Field_(mathematics)

  • Artin L-function
  • Type of Dirichlet series associated to number field extensions

    one. He predicted existence of Stark units whose roots should generate Kummer extensions of K {\displaystyle K} and having implications for Hilbert's

    Artin L-function

    Artin_L-function

  • Glossary of areas of mathematics
  • group of the geometry. Knot theory part of topology dealing with knots Kummer theory provides a description of certain types of field extensions involving

    Glossary of areas of mathematics

    Glossary_of_areas_of_mathematics

AI & ChatGPT searchs for online references containing KUMMER SUM

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KUMMER SUM

  • Grishmak
  • Boy/Male

    Hindu, Indian

    Grishmak

    Summer

    Grishmak

  • Suvi
  • Girl/Female

    Hindu

    Suvi

    Summer

    Suvi

  • Haf
  • Girl/Female

    Australian

    Haf

    Summer

    Haf

  • Sumter
  • Surname or Lastname

    English

    Sumter

    English : variant of Sumpter.Fort Sumter, SC, was named in honor of Thomas Sumter, known as the ‘Gamecock of the Revolution’ for the fear he inspired in the British and Tory forces and the pivotal role he played in key American victories. Born in 1734 near Charlottesville, VA, he was of Welsh heritage; his ancestors probably emigrated to America in the late 17th century.

    Sumter

  • Hammer
  • Boy/Male

    Australian, Norse, Scandinavian

    Hammer

    Hammer

    Hammer

  • SUMMER
  • Female

    English

    SUMMER

    English name derived from the vocabulary word, summer, from Old English sumor, SUMMER means "summer," the hot season of the year.

    SUMMER

  • Summer
  • Surname or Lastname

    English and German

    Summer

    English and German : from Middle English sum(m)er, Middle High German sumer ‘summer’, hence a nickname for someone of a warm or sunny disposition, or for someone associated with the season of summer in some other way.English : assimilated variant of Sumner.English : assimilated variant of Sumpter.Irish (Leinster and Munster) : Anglicization (part translation) of Gaelic Ó Samhraidh ‘descendant of Samhradh’, a byname meaning ‘summer’. The Gaelic name is also Anglicized as O’Sawrie, O’Sawra.German : from Middle High German summer ‘woven basket’ and, by extension, a measure of grain; also ‘drum’, hence a metonymic occupational name or nickname from any of these senses.

    Summer

  • KUZMIR
  • Male

    Yiddish

    KUZMIR

    (קאזמיר) Yiddish form of Polish Kazimierz, KUZMIR means "commands peace."

    KUZMIR

  • Suvi | ஸுவீ 
  • Girl/Female

    Tamil

    Suvi | ஸுவீ 

    Summer

    Suvi | ஸுவீ 

  • Summer
  • Girl/Female

    English American

    Summer

    Born during the summer.

    Summer

  • Cammer
  • Surname or Lastname

    English

    Cammer

    English : variant of Comer.Respelling of German Kammer.

    Cammer

  • Sommer
  • Girl/Female

    American, Australian, British, Christian, English, German

    Sommer

    Summer Season; Place Name

    Sommer

  • Summer
  • Girl/Female

    American, Arabic, Australian, British, Chinese, English, Hebrew

    Summer

    The Warmest Season of the Year; Summer Season; Name of the Season; Summer; The Hot Season of the Year

    Summer

  • Summers
  • Surname or Lastname

    English

    Summers

    English : patronymic from Summer 1.Irish (Sligo) : adopted as an English equivalent of Gaelic Ó Somacháin ‘descendant of Somachán’, a nickname meaning ‘gentle’, ‘innocent’.Americanized form of some like-sounding Ashkenazic Jewish name.

    Summers

  • Sommer
  • Surname or Lastname

    English and Irish

    Sommer

    English and Irish : variant of Summer.German and Danish : from Middle German sumer, Danish, Norwegian sommer ‘summer’, a nickname for someone of a warm disposition, or for someone associated with the season in some other way or from living in a sunny place, in some instances a metonymic occupational name for a basketweaver or a drummer, from Middle High German sum(b)er, sum(m)er ‘basket’, ‘basketry’, ‘drum’.Jewish (Ashkenazic) : ornamental name from German Sommer ‘summer’. Like the other seasonal names, this was also one of the group of names that were bestowed on Jews more or less at random by government officials in 18th- and 19th-century central Europe.

    Sommer

  • Greeshm
  • Boy/Male

    Hindu, Indian

    Greeshm

    Summer

    Greeshm

  • Greashma
  • Girl/Female

    Hindu, Indian

    Greashma

    Summer

    Greashma

  • SOMMER
  • Female

    German

    SOMMER

     German equivalent of English Summer, SOMMER means "summer." Compare with another form of Sommer.

    SOMMER

  • SOMMER
  • Female

    English

    SOMMER

     Variant spelling of English Summer, SOMMER means "summer." Compare with another form of Sommer.

    SOMMER

  • Sumner
  • Surname or Lastname

    English

    Sumner

    English : occupational name for a summoner, an official who was responsible for ensuring the appearance of witnesses in court, Middle English sumner, sumnor.William Sumner came to Dorchester, MA, from England in about 1635. His descendants include U.S. Senator Charles Sumner, a major force in the struggle to end slavery, who was born in 1811 in Boston.

    Sumner

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Online names & meanings

  • Anchal
  • Boy/Male

    Indian, Sanskrit

    Anchal

    Valley; Hamlet

  • Asamati
  • Boy/Male

    Indian, Sanskrit

    Asamati

    Unequalled; Supreme; Divine

  • Mustali
  • Boy/Male

    Arabic, Muslim

    Mustali

    High; Elevated; Superior

  • Subh
  • Boy/Male

    Hindu

    Subh

    Auspicious

  • Sukrida
  • Girl/Female

    Hindu, Indian, Marathi, Sanskrit

    Sukrida

    Sporting; An Angel

  • Antea
  • Girl/Female

    Greek

    Antea

    Son of Poseidon.

  • Amzi
  • Boy/Male

    Biblical

    Amzi

    Strong, mighty'.

  • Saib
  • Boy/Male

    Arabic, Muslim, Sindhi

    Saib

    Forsaken; Abandoned; Appropriate; Correct; The Wind Coming with Rain

  • Bakhtawar
  • Girl/Female

    Muslim/Islamic

    Bakhtawar

    Fortunate Lucky

  • Sanjev
  • Boy/Male

    Hindu, Indian

    Sanjev

    Long Life

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Other words and meanings similar to

KUMMER SUM

AI search in online dictionary sources & meanings containing KUMMER SUM

KUMMER SUM

  • Scummer
  • n.

    An instrument for taking off scum; a skimmer.

  • Number
  • n.

    To give or apply a number or numbers to; to assign the place of in a series by order of number; to designate the place of by a number or numeral; as, to number the houses in a street, or the apartments in a building.

  • Hammer
  • n.

    Something which in firm or action resembles the common hammer

  • Summery
  • a.

    Of or pertaining to summer; like summer; as, a summery day.

  • Summertree
  • n.

    A summer. See 2d Summer.

  • Hammer
  • v. t.

    To beat with a hammer; to beat with heavy blows; as, to hammer iron.

  • Summer
  • v.

    One who sums; one who casts up an account.

  • Summer
  • v. i.

    To pass the summer; to spend the warm season; as, to summer in Switzerland.

  • Lumber
  • b. t.

    To fill or encumber with lumber; as, to lumber up a room.

  • Hummel
  • a.

    Having no awns or no horns; as, hummelcorn; a hummel cow.

  • Umber
  • a.

    Of or pertaining to umber; resembling umber; olive-brown; dark brown; dark; dusky.

  • Number
  • n.

    A numeral; a word or character denoting a number; as, to put a number on a door.

  • Summer
  • v. t.

    To keep or carry through the summer; to feed during the summer; as, to summer stock.

  • Hammer
  • v. i.

    To be busy forming anything; to labor hard as if shaping something with a hammer.

  • Gold-hammer
  • n.

    The yellow-hammer.

  • Summer
  • n.

    A large stone or beam placed horizontally on columns, piers, posts, or the like, serving for various uses. Specifically: (a) The lintel of a door or window. (b) The commencement of a cross vault. (c) A central floor timber, as a girder, or a piece reaching from a wall to a girder. Called also summertree.

  • Summer-fallow
  • v. t.

    To plow and work in summer, in order to prepare for wheat or other crop; to plow and let lie fallow.

  • Hammer
  • v. t.

    To form or forge with a hammer; to shape by beating.

  • Umber
  • v. t.

    To color with umber; to shade or darken; as, to umber over one's face.