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Topics referred to by the same term
Reciprocity theorem may refer to: Quadratic reciprocity, a theorem about modular arithmetic Cubic reciprocity Quartic reciprocity Artin reciprocity Weil
Reciprocity_theorem
Gives conditions for the solvability of quadratic equations modulo prime numbers
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations
Quadratic_reciprocity
Gives a functional equation satisfied by the generating function of any rational cone
Stanley's reciprocity theorem, named after the mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the integer-point
Stanley's_reciprocity_theorem
Theorem in classical electromagnetism
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities
Reciprocity (electromagnetism)
Reciprocity_(electromagnetism)
Property of a circuit
Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points. The reciprocity theorem states that the
Reciprocity (electrical networks)
Reciprocity_(electrical_networks)
Mathematical theorem
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms
Artin_reciprocity
Topics referred to by the same term
electromagnetism Reciprocity (electrical networks), reciprocity theorem as it relates to current and voltage in electrical networks Reciprocity (network science)
Reciprocity
Conditions under which the congruence x^3 equals p (mod q) is solvable
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q)
Cubic_reciprocity
context of Riemannian geometry. A quote from Ellis: "The core of the reciprocity theorem is the fact that many geometric properties are invariant when the
Etherington's reciprocity theorem
Etherington's_reciprocity_theorem
Duality between the process of restricting and inducting in representation theory
mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducing
Frobenius_reciprocity
Ehrhart polynomial (see below), all special cases of Stanley's general Reciprocity Theorem. The chromatic polynomial P ( G , n ) {\displaystyle P(G,n)} counts
Order_polynomial
Conditions in number theory
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence
Quartic_reciprocity
Topics referred to by the same term
Frobenius theorem (real division algebras) in abstract algebra characterizing the finite-dimensional real division algebras Frobenius reciprocity theorem in
Frobenius_theorem
In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusually large number of proofs. Several hundred
Proofs of quadratic reciprocity
Proofs_of_quadratic_reciprocity
theory) Sperner's theorem (combinatorics) Stanley's reciprocity theorem (combinatorics) Star of David theorem (combinatorics) Stirling's theorem (mathematical
List_of_theorems
Maxwell's reciprocity theorem. In electromagnetism the concept is known as Lorentz reciprocity, a special case of which is the reciprocity theorem of electrical
Reciprocity_(engineering)
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Directional variation in strength of radio waves
antenna when used for transmitting. This is a consequence of the reciprocity theorem of electromagnetics and is proved below. Therefore, in discussions
Radiation_pattern
Mathematical law, a generalization of quadratic reciprocity
In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle
Reciprocity_law
Theorem on modular exponentiation
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers
Euler's_theorem
Relation between sides of a right triangle
{\displaystyle c^{2}=a^{2}+b^{2}.} This theorem may have more known proofs than any other (the law of quadratic reciprocity being another contender for that
Pythagorean_theorem
Mathematical theorem
for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations
Symmetry of second derivatives
Symmetry_of_second_derivatives
Process of extending a representation of a subgroup to the parent group
finite groups and finite-dimensional representations, the Frobenius reciprocity theorem states that, given representations σ of H and ρ of G, the space of
Induced_representation
the law of quadratic reciprocity as the "fundamental theorem" of quadratic residues. There are also a number of "fundamental theorems" that are not directly
List of theorems called fundamental
List_of_theorems_called_fundamental
Relation of an integral polytope's volume to how many integer points it encloses
what is called a multivariate quasi-polynomial. An Ehrhart-type reciprocity theorem will also hold for such a counting function. Counting the number
Ehrhart_polynomial
Topics referred to by the same term
several theorems known as the Helmholtz theorem: Helmholtz decomposition, also known as the fundamental theorem of vector calculus Helmholtz reciprocity in
Helmholtz_theorem
Says when a natural number is the sum of three squares of integers
quadratic reciprocity law, Dirichlet's theorem on arithmetic progressions, and the equivalence class of the trivial ternary quadratic form. This theorem can
Legendre's three-square theorem
Legendre's_three-square_theorem
American mathematician (born 1944)
Exponential formula Order polynomial Stanley decomposition Stanley's reciprocity theorem "Misc". MIT. Stanley, Richard (2017). "Curriculum Vitae". Retrieved
Richard_P._Stanley
Theorem on prime numbers
In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers
Wilson's_theorem
Principle in optics relating light rays and their reverse rays
the electromagnetic nature of light became known. The Helmholtz reciprocity theorem has been rigorously proven in a number of ways, generally making
Helmholtz_reciprocity
Technique to measure resistivity and Hall coefficient
{\displaystyle e^{-\pi R_{12,34}/R_{s}}+e^{-\pi R_{23,41}/R_{s}}=1} The reciprocity theorem tells us that R A B , C D = R C D , A B {\displaystyle R_{AB,CD}=R_{CD
Van_der_Pauw_method
In mathematics, Drinfeld reciprocity, introduced by Drinfeld (1974), is a correspondence between eigenforms of the moduli space of Drinfeld modules and
Drinfeld_reciprocity
prism. A prism coupler may be explained in terms of the reciprocity theorem. The reciprocity theorem permits the relative power coupled into the thin film
Prism_coupler
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
British mathematician who proved Fermat's Last Theorem
specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal
Andrew_Wiles
Measure of the "spread" of light in an optical system
etendue. The conservation of etendue in free space is related to the reciprocity theorem for view factors. The conservation of etendue discussed above applies
Etendue
Aesthetic value of mathematics
of proofs published. Another theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss
Mathematical_beauty
Relation between relative derivatives of three variables
rule, cyclic relation, cyclical rule, Euler's chain rule, or the reciprocity theorem, is a formula which relates partial derivatives of three interdependent
Triple_product_rule
Number divisible only by 1 and itself
quadratic reciprocity, a statement that concerns the existence of square roots modulo integer prime numbers. Early attempts to prove Fermat's Last Theorem led
Prime_number
German mathematician (1807–1894)
helpful to Gotthold Eisenstein in formulating a proof of the quadratic reciprocity theorem. Stern was interested in primes that cannot be expressed as the sum
Moritz_Abraham_Stern
Relation between properties of diodes
Optoelectronic reciprocity relations relate properties of a diode under illumination to the photon emission of the same diode under applied voltage. The
Reciprocity_(optoelectronic)
Astronomical measurement in mathematics
diameter distance D A {\displaystyle D_{A}} by the Etherington's reciprocity theorem: D L = ( 1 + z ) 2 D A {\displaystyle D_{L}=(1+z)^{2}D_{A}} where
Luminosity_distance
Law in algebraic number theory
theory Eisenstein's reciprocity law is a reciprocity law that extends the law of quadratic reciprocity and the cubic reciprocity law to residues of higher
Eisenstein_reciprocity
first principles, and Dedekind's reciprocity law is equivalent to quadratic reciprocity. Rewriting the reciprocity law as 12 b c ( s ( b , c ) + s (
Dedekind_sum
Type of radio propagation
ionosphere is far too complex and constantly changing to support the reciprocity theorem. The path is never exactly the same in both directions. In brief
Non-line-of-sight_propagation
Sub-discipline of electrical engineering
relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain. Network graphs: matrices associated with graphs; incidence
Electronics_engineering
Topics referred to by the same term
rule (AKA Euler's chain rule, triple product rule, cyclic relation, reciprocity theorem), relating partial derivatives of three interdependent variables
Chain_rule_(disambiguation)
German polymath and scholar (1777–1855)
composition law, the law of quadratic reciprocity, and proved the triangular case of the Fermat polygonal number theorem. He also contributed to the theory
Carl_Friedrich_Gauss
Imaging and diffraction using electrons that pass through samples
correct electron chromatic aberration. The optical reciprocity theorem, or principle of Helmholtz reciprocity, generally holds true for elastically scattered
Transmission electron microscopy
Transmission_electron_microscopy
Finnish engineer, academic, author, and opera singer
the Detection of the Magnetic Heart Vector – An Application of the Reciprocity Theorem (doctoral thesis) and the book that he co-authored with Robert Plonsey:
Jaakko_A._Malmivuo
Internal magnetic field generated by a magnet
first magnet in the demagnetizing field Hd(2) of the second is The reciprocity theorem states that Formally, the solution of the equations for the potential
Demagnetizing_field
Reciprocal work theorem in engineering
displacement at point 1 of Δ Q 1 {\displaystyle \Delta _{Q1}} . Betti's reciprocity theorem states that: P Δ Q 1 = Q Δ P 2 . {\displaystyle P\,\Delta _{Q1}=Q\
Betti's_theorem
Theorem on the number of primes in arithmetic sequences
The general form of the theorem was first conjectured by Legendre in his attempted unsuccessful proofs of quadratic reciprocity — as Gauss noted in his
Dirichlet's theorem on arithmetic progressions
Dirichlet's_theorem_on_arithmetic_progressions
Branch of number theory
contributions to Fermat's last theorem, for which he proved the cases n = 5 and n = 14, and to the biquadratic reciprocity law. The Dirichlet divisor problem
Algebraic_number_theory
Cyclotomic field Cubic field Biquadratic field Quadratic reciprocity Ideal class group Dirichlet's unit theorem Discriminant of an algebraic number field Ramification
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Formula concerning prime numbers
prime field for more details. Because the modulus is prime, Lagrange's theorem applies: a polynomial of degree k can only have at most k roots. In particular
Euler's_criterion
Artin L-function Artin reciprocity Artin–Rees lemma Artin representation Artin–Schreier theorem Artin–Schreier theory Artin's theorem on induced characters
List of things named after Emil Artin
List_of_things_named_after_Emil_Artin
Physics theory
choice of principle to derive the equations of the CMT. Either the reciprocity theorem or the variational principle have been used. The choice of orthogonality
Coupled_mode_theory
Conjectures connecting number theory and geometry
point of the program was Emil Artin's reciprocity law, which generalizes quadratic reciprocity. The Artin reciprocity law applies to a Galois extension of
Langlands_program
Device that transmits and receives radio waves
differ between receiving and transmitting. This equivalence follows reciprocity theorem of electromagnetics. Therefore, in discussions of antenna properties
Antenna_(radio)
Overview of and topical guide to combinatorics
sieving Schrödinger method Exponential generating function Stanley's reciprocity theorem Binomial coefficients and their properties Combinatorial proof Double
Outline_of_combinatorics
On the action of ideles of imaginary quadratic fields on the values of modular functions
In mathematics, Shimura's reciprocity law, introduced by Shimura (1971), describes the action of ideles of imaginary quadratic fields on the values of
Shimura's_reciprocity_law
Austrian-American mathematician (1921-2002)
Mautner, F. I. (July 1951). "A Generalization of the Frobenius Reciprocity Theorem". Proc Natl Acad Sci U S A. 37 (7): 431–435. doi:10.1073/pnas.37
Friederich_Ignaz_Mautner
Branch of algebraic number theory concerned with abelian extensions
from L to F. This isomorphism is named the reciprocity map. The existence theorem states that the reciprocity map can be used to give a bijection between
Class_field_theory
Cosmological formulas for expanding universe
{\displaystyle z} is the measured redshift, in accordance with Etherington's reciprocity theorem (see below). (also known as "lookback time" or "lookback distance")
Distance_measure
Branch of physics
time-domain integral-equation technique that is formulated via the Lorentz reciprocity theorem. Since the CdH-MoM heavily relies on the Cagniard-deHoop method,
Computational electromagnetics
Computational_electromagnetics
Theorem in algebraic number theory
fundamental class in H2(Gal(K/F),IK) and a reciprocity law map from IK to Gal(L/K). The Shafarevich–Weil theorem states that the class of the extension Gal(L/F)
Shafarevich–Weil_theorem
Fundamental result in the branch of mathematics known as character theory
Brauer's theorem, notably by Robert Boltje. Using Frobenius reciprocity, Brauer's induction theorem leads easily to his fundamental characterization of characters
Brauer's theorem on induced characters
Brauer's_theorem_on_induced_characters
Mathematical fallacy
4.20. ("Schoolboy binomial theorem")". Number Theory: A Contemporary Introduction (PDF). Chapter 4. Quadratic Reciprocity : 7. Proof of the Second Supplement
Freshman's_dream
Subfield of computer science and logic
automated reasoning are automated theorem proving (and the less automated but more pragmatic subfield of interactive theorem proving) and automated proof checking
Automated_reasoning
in his proof of Chebotarev's density theorem, and used shortly afterwards by Artin to prove his reciprocity theorem. For general layers E,F there is an
Class_formation
Mathematical concept
places, i.e. equivalent over every completion of the field. Artin's reciprocity law implies a description of the abelianization of the absolute Galois
Global_field
Surname list
(restaurant), in Chicago, United States Feld-Tai reciprocity or Feld-Tai reciprocity theorem; in Reciprocity (electromagnetism) Feldt Felt (disambiguation)
Feld
In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed
Weil_reciprocity_law
American mathematician (1904–1988)
of water wave fronts in hydrodynamics, and the proof of quadratic reciprocity theorem in number theory from 'hydrodynamical' perspective. Lewy was elected
Hans_Lewy
Topics referred to by the same term
an eigenvalue algorithm to perform QR decomposition Quadratic reciprocity, a theorem from modular arithmetic Quasireversibility, a property of some queues
QR
Topics referred to by the same term
Theorema Egregium, "Remarkable Theorem", best-known example Aureum Theorema, "Golden Theorem", better-known as quadratic reciprocity Search for "theorema" on
Theorema_(disambiguation)
Branch of pure mathematics
stated the law of quadratic reciprocity. He also conjectured what amounts to the prime number theorem and Dirichlet's theorem on arithmetic progressions
Number_theory
his reciprocity law. 1924 Artin introduces Artin L-functions. 1926 Nikolai Chebotaryov proves his density theorem. 1927 Artin proves his reciprocity law
Timeline of class field theory
Timeline_of_class_field_theory
relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain. Additional basic fundamental in electrical are to
Education and training of electrical and electronics engineers
Education_and_training_of_electrical_and_electronics_engineers
Formal power series
Probability-generating function Generating function transformation Stanley's reciprocity theorem Integer partition Combinatorial principles Cyclic sieving Z-transform
Generating_function
Sum in algebraic number theory
}\right)}}.} Gauss sums can be used to prove quadratic reciprocity, cubic reciprocity, and quartic reciprocity. Gauss sums can be used to calculate the number
Gauss_sum
British mathematician (1908–1994)
German refugees, giving many shelter in their own home. Etherington's reciprocity theorem Wedderburn–Etherington number "Biography of I. M. H. Etherington"
Ivor_Etherington
Type of infinitesimal in calculus
y}},{\frac {\partial Q}{\partial z}}\right)} can be made. The gradient theorem states ∫ i f d Q = ∫ i f ∇ Q ( r ) ⋅ d r = Q ( f ) − Q ( i ) {\displaystyle
Exact_differential
Hilbert ring Hilbert–Samuel function Hilbert projection theorem Hilbert R-tree Hilbert reciprocity Hilbert scheme Hilbert space Hilbert dimension Projective
List of things named after David Hilbert
List_of_things_named_after_David_Hilbert
German mathematician (1823–1852)
Eisenstein integer Eisenstein prime Eisenstein reciprocity Eisenstein sum Eisenstein series Eisenstein's theorem Eisenstein triple Eisenstein–Kronecker number
Gotthold_Eisenstein
Generalization of polynomials
Sanyal, Raman (2018), "Section 4.5: Quasipolynomials", Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics, Graduate Studies
Quasi-polynomial
Canadian electrical engineer and physicist (1924–1998)
and Reply by D. Schieber 1974 Comments on "The Use of the Lorentz Reciprocity Theorem to Prove Equality of the Open Circuit Voltages of a Receiving Dipole
James_R._Wait
Soviet mathematician (1894–1947)
was a Soviet mathematician. He is best known for the Chebotaryov density theorem. He was a student of Dmitry Grave. Chebotaryov worked on the algebra of
Nikolai_Chebotaryov
crosscorrelation for reconstructing Green's function using wave field reciprocity theorem in a lossless, 3D heterogeneous medium. Traces are most often extended
Seismic_interferometry
Integer that is a perfect square modulo some integer
Using Dirichlet's theorem on primes in arithmetic progressions, the law of quadratic reciprocity, and the Chinese remainder theorem (CRT) it is easy to
Quadratic_residue
Antenna testing techniques
currents and tensions is far from immediate. However, using the reciprocity theorem, it is possible to prove that the Thévenin equivalent circuit of
Antenna_measurement
American mathematician
Sturmfels at UC-Berkeley, and has been noted for work on Stanley's reciprocity theorem and tight spans. His 2004 paper, "Tropical Convexity", with Sturmfels
Mike_Develin
French mathematician (1906-1998)
leading to the Mordell–Weil theorem (1928, and shortly applied in Siegel's theorem on integral points). Mordell's theorem had an ad hoc proof; Weil began
André_Weil
Result in mathematical invariant theory
In mathematics, Hermite's law of reciprocity, introduced by Hermite (1854), states that the degree m covariants of a binary form of degree n correspond
Hermite_reciprocity
mathematician. Bergman–Weil formula Borel–Weil theorem Chern–Weil homomorphism Chern–Weil theory De Rham–Weil theorem Weil's explicit formula Hasse-Weil bound
List of things named after André Weil
List_of_things_named_after_André_Weil
Frobenius reciprocity Frobenius solution to the hypergeometric equation Frobenius splitting Frobenius theorem (differential topology) Frobenius theorem (real
List of things named after Ferdinand Georg Frobenius
List_of_things_named_after_Ferdinand_Georg_Frobenius
Japanese mathematician (1930–2019)
Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem. Gorō Shimura was born in Hamamatsu, Japan, on 23 February 1930. Shimura
Goro_Shimura
1090/pcms/013/08. ISBN 9780821837368. Stanley, Richard (1974). "Combinatorial reciprocity theorems". Advances in Mathematics. 14 (2): 194–253. doi:10.1016/0001-8708(74)90030-9
History_of_combinatorics
} Euler's theorem Euler's theorem states that if n and a are coprime positive integers, then aφ(n) is congruent to 1 mod n. Euler's theorem generalizes
Glossary_of_number_theory
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RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
RECIPROCITY THEOREM
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