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See searches and references containing STANDARD L-FUNCTION!STANDARD L-FUNCTION
Mathematical concept
mathematics, the term standard L-function refers to a particular type of automorphic L-function described by Robert P. Langlands. Here, standard refers to the
Standard_L-function
S-shaped curve
+\infty } is L {\displaystyle L} . The exponential function with negated argument ( e − x {\displaystyle e^{-x}} ) is used to define the standard logistic
Logistic_function
Mathematical Theory
constructed their convolution L-functions, now thought of as the Langlands L-function associated to the tensor product of standard representation of GL(2) with
Rankin–Selberg_method
Mathematical concept
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive
Automorphic_L-function
Function from the limited hyperreal to the real numbers
the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds
Standard_part_function
Description of the average spectral sensitivity of human visual perception of brightness
efficiency function generally refers to the photopic luminous efficiency function. The CIE photopic luminous efficiency function y(λ) or V(λ) is a standard function
Luminous_efficiency_function
Probability distribution
σ2. The standard approach to this problem is the maximum likelihood method, which requires maximization of the log-likelihood function: lnℒ(μ,σ2)=∑i=1nlnf(xi∣μ
Normal_distribution
Space of bounded sequences
Σ , μ ) {\displaystyle L^{\infty }=L^{\infty }(X,\Sigma ,\mu )} , the vector space of essentially bounded measurable functions with the essential supremum
L-infinity
Sigmoid shape special function
error function has the following interpretation: for a real random variable Y {\displaystyle Y} that is normally distributed with mean 0 and standard deviation
Error_function
Uniform distribution on an interval
density f=dPrX(n)dλ: f(t)=n1L(tL)n−1=ntn−1Ln11[0,L](t), where 11[0,L] is the indicator function of [0,L]. The confidence interval given before is mathematically
Continuous uniform distribution
Continuous_uniform_distribution
C standard library header file
are a group of functions in the standard library of the C programming language implementing basic mathematical functions. The C++ standard library, which
C_mathematical_functions
Measure of variation in statistics
_{i=1}^{N}p_{i}x_{i}\,.} The standard deviation of a continuous real-valued random variable X with probability density function p(x) is σ = ∫ X ( x − μ )
Standard_deviation
Standardized literary variety of Arabic
Modern Standard Arabic (MSA) or Modern Written Arabic (MWA) is the variety of standardized, literary Arabic that developed in the Arab world in the late
Modern_Standard_Arabic
Method of solution to differential equations
that if L is a linear differential operator, then the Green's function G is the solution of the equation LG=δ, where δ is Dirac's delta function; the solution
Green's_function
Description of continuous random distribution
probability distribution function and probability function can also denote the probability density function. However, this use is not standard among probabilists
Probability_density_function
Probability that random variable X is less than or equal to x
statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability
Cumulative distribution function
Cumulative_distribution_function
Continuous function that is not absolutely continuous
function is the standard example of a singular function. The Cantor function is also a standard example of a function with bounded variation but, as mentioned
Cantor_function
Point to which functions converge in analysis
f(x) to every input x. We say that the function has a limit L at an input p, if f(x) gets closer and closer to L as x moves closer and closer to p. More
Limit_of_a_function
Arbitrary-precision calculator supporting interactive and scripted use
in its argument are also built-in. bc's standard math library (defined with the -l option) contains functions for calculating sine, cosine, arctangent
Bc_(programming_language)
Statistics function
In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the
Q-function
Concept in probability theory and statistics
its moment generating function MX(t) and the two-sided Laplace transform of its probability density function fX(x) holds: MX(t)=ℒ{fX}(−t), since the PDF's
Moment_generating_function
Set of quantities in probability theory
cumulant generating function (CGF) K(t), which is a generating function that is the natural logarithm of the moment generating function: K ( t ) = log
Cumulant
Canadian mathematician
Langlands group Langlands–Shahidi method Local Langlands conjectures Standard L-function Taniyama group Alex Bellos (March 20, 2018). "Abel Prize 2018: Robert
Robert_Langlands
Russian cryptographic hash function
The GOST hash function, defined in the standards GOST R 34.11-94 and GOST 34.311-95 is a 256-bit cryptographic hash function. It was initially defined
GOST_(hash_function)
Statistical function that defines the quantiles of a probability distribution
the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the quantile function of a distribution
Quantile_function
Multivalued function in mathematics
) 6 L 1 3 + L 2 ( − 12 + 36 L 2 − 22 L 2 2 + 3 L 2 3 ) 12 L 1 4 + ⋯ = L 1 − L 2 + ∑ ℓ = 1 ∞ 1 L 1 ℓ ∑ m = 1 ℓ ( − 1 ) ℓ − m [ ℓ ℓ − m + 1 ] m ! L 2 m
Lambert_W_function
Mathematician at the University of Minnesota
Society in 2019, and was awarded a Simons Fellow in 2024. Degree 16 standard L-function of GSp(2)×GSp(2). Mem. Amer. Math. Soc. 123 (1996), no. 588, viii+196
Dihua_Jiang
Special mathematical functions defined on the surface of a sphere
[ L z , L + ] = L + , [ L z , L − ] = − L − , [ L + , L − ] = 2 L z . {\displaystyle [L_{z},L_{+}]=L_{+},\quad [L_{z},L_{-}]=-L_{-},\quad [L_{+},L_{-}]=2L_{z}
Spherical_harmonics
Discrete-variable probability distribution
a probability mass function (PMF), discrete probability density function, probability function, or frequency function is a function that gives the probability
Probability_mass_function
Mathematical function
peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to
Gaussian_function
Ratio of polynomial functions
is L. The set of rational functions over a field K is a field, the field of fractions of the ring of the polynomial functions over K. A function f is
Rational_function
Mathematical function whose derivative exists
x0+δ), f(x)−f(x0)x−x0∈(L−ϵ,L+ϵ). In other words, the graph of f has a non-vertical tangent line at the point (x0,f(x0)). The function f is said to be differentiable
Differentiable_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
General-purpose functional programming language
functional languages, a key feature of Standard ML is the function, which is used for abstraction. The factorial function can be expressed as follows: fun factorial
Standard_ML
Theory of forces and subatomic particles
arbitrary function of spacetime. The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1) × SU(2)L, L EW = Q ¯ L j i γ μ D μ Q L j +
Standard_Model
Analytic function in mathematics
Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function ζ(s) is a function of a complex
Riemann_zeta_function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Chemical compound
magnesium ions. One small study reports that magnesium L-threonate improves cognitive function in healthy adults, compared to placebo; other magnesium
Magnesium_L-threonate
Probability distribution
the standard distribution, the cumulative distribution function simplifies to arctangent function arctan(x): F(x;0,1)=1πarctan(x)+12 The standard Cauchy
Cauchy_distribution
Type of mathematical expression
substitution to the substituted value is a function, called a polynomial function; see § Polynomial functions. This can be expressed more concisely by using
Polynomial
Colour space defined by the CIE in 1931
accurate luminosity curves; see Luminosity function#Improvements to the standard. Harris, A. C.; Weatherall, I. L. (September 1990). "Objective evaluation
CIE_1931_color_space
French mathematician (1921–2016)
Commutation theorem for traces Plancherel theorem for spherical functions Standard L-function "Décès de Roger Godement | Société Mathématique de France".
Roger_Godement
Functions of an angle
extend the sine and cosine functions to functions whose domain is the whole real line, geometrical definitions using the standard unit circle (i.e., a circle
Trigonometric_functions
Smooth and compactly supported function
used as cutoff functions, for example functions that are equal to 1 on a prescribed set and vanish outside a larger set, and as standard examples of kernels
Bump_function
How many standard deviations apart from the mean an observed datum is
{\displaystyle \gamma } , i.e. Pr ( L < X < U ) = γ , {\displaystyle \Pr(L<X<U)=\gamma ,} For the standard score Z of X it gives: Pr ( L − μ σ < Z < U − μ σ ) = γ
Standard_score
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/), denoted by sinc(x), is defined as either sinc(x)=sinxx or sinc(x)=sinπxπx, the
Sinc_function
Function studied by Ramanujan
of weight 12, it gives rise to an L {\displaystyle L} -function, called Ramanujan's L {\displaystyle L} -function. It is defined for R e ( s ) > 13 /
Ramanujan_tau_function
Extension of the factorial function
accepted standard for whether the function name should be written "gamma function" or "Gamma function" (some authors simply write "Γ-function"). The alternative
Gamma_function
Generalized function whose value is zero everywhere except at zero
mathematical analysis, the Dirac delta function (or 𝜹 distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value
Dirac_delta_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
American mathematician
explicit relation between automorphic periods and central values of standard L-functions. This integral representation has since become a fundamental tool
Solomon_Friedberg
Type of topological space
Bochner spaces are a generalization of the concept of L p {\displaystyle L^{p}} spaces to functions whose values lie in a Banach space which is not necessarily
Bochner_space
Standard for HDTV image encoding and signal characteristics
Thus the standard opted for a piecewise function that combines a simple linear function V=aL for low light levels and a shifted power law ((L+c)/(1+c))γ
Rec._709
Function related to statistics and probability theory
distribution with density function f (a function of x) which depends on a parameter θ. Then the function ℒ(θ∣x)=fθ(x), considered as a function of θ, is the likelihood
Likelihood_function
System used to generate stable voltages, that may be used to define a volt
function of the junction geometry, the temperature, and any residual magnetic field inside the magnetic shields that are used with voltage standard devices
Josephson_voltage_standard
Value approached by a mathematical object
value of the function f can be made arbitrarily close to L, by choosing x sufficiently close to c. Alternatively, the fact that a function f approaches
Limit_(mathematics)
Hash function that is suitable for use in cryptography
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n {\displaystyle n}
Cryptographic_hash_function
Microeconomic function
the prices of other goods, a more technical exposition of the standard demand function. It is a solution to the utility maximization problem of how the
Marshallian_demand_function
Set of cryptographic hash functions
publication date in 2011). In March 2012, the standard was updated in FIPS PUB 180-4, adding the hash functions SHA-512/224 and SHA-512/256, and describing
SHA-2
Function which is integrable on its domain
importance of such functions lies in the fact that their function space is similar to p-integrable function spaces ( L p {\textstyle L^{p}} spaces), but
Locally_integrable_function
C programming language standard, 2011 revision
literals). Removal of the gets() function (in favor of safer fgets()), which was deprecated in the previous C language standard revision, ISO/IEC 9899:1999/Cor
C11_(C_standard_revision)
Cryptographic hash function
a cryptographic hash function. It was designed by Vincent Rijmen (co-creator of the Advanced Encryption Standard) and Paulo S. L. M. Barreto, who first
Whirlpool_(hash_function)
C function to format and output text
is a C standard library function and is also a Linux terminal (shell) command that formats text and writes it to standard output. The function accepts
Printf
General-purpose programming language
of the code that defines the function. The next line of code calls (diverts execution to) the C standard library function printf with the address of the
C_(programming_language)
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Connected input and output streams for computer programs
End Function When applying the System.Diagnostics.Process class one can use the instance properties StandardInput, StandardOutput, and StandardError
Standard_streams
Power series derived from a discrete probability distribution
generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random
Probability generating function
Probability_generating_function
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Special functions
In special functions, a topic in mathematics, spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and—like the usual
Spin-weighted spherical harmonics
Spin-weighted_spherical_harmonics
Mathematical conjecture on the Riemann zeta function
1007/s10240-010-0025-8. S2CID 14155294. Nelson, Paul D. (2021-09-30). "Bounds for standard $L$-functions". arXiv:2109.15230 [math.NT]. Hartnett, Kevin (2022-01-13). "Mathematicians
Lindelöf_hypothesis
System of identifying electrical power devices
device numbers are enumerated in ANSI/IEEE Standard C37.2 Standard for Electrical Power System Device Function Numbers, Acronyms, and Contact Designations
ANSI_device_numbers
Generalized version of classical Green's function
G(L,L') can be expressed by a single index (L'-L) defined as G ( L , L ′ ) = G ( 0 , L − L ′ ) = G ( L ′ − L ) ( 10 ) {\displaystyle G(L,L')=G(0,L-L')=G(L'-L)\qquad
Multiscale_Green's_function
Set of cryptographic hash functions
for the SHA-3 standard, compared to the submission. The changes caused some turmoil. The hash function competition called for hash functions at least as
SHA-3
Cryptographic tool
which meet Federal Information Processing Standards. H a s h {\displaystyle {\mathsf {Hash}}} hash function ( h L e n {\displaystyle {\mathsf {hLen}}} denotes
Mask_generation_function
American mathematician (1942–2012)
"Poles of Standard L-functions" at the 1990 International Congress of Mathematicians in Kyoto. In 2003, the conference "Automorphic Representations, L-Functions
Stephen_Rallis
Mathematical function for the probability a given outcome occurs in an experiment
likely different results are. Formally, it is a probability measure: a function that assigns probabilities to events in a way that satisfies the axioms
Probability_distribution
Function in statistics
statistics, the logit (logistic unit) or log-odds function is the quantile function associated with the standard logistic distribution. It has many uses in data
Logit
2011 edition of the C++ programming language standard
the C++ Standard Library, incorporating most of the C++ Technical Report 1 (TR1) libraries, except the library of mathematical special functions. C++11
C++11
C programming language standard draft planned for release in 2029
at least 2001 and later became part of the POSIX.1-2008 standard. Add bit utility functions / macros / types in header <stdbit.h> to examine many integer
C29_(C_standard_revision)
Color space with color-opponent values
easily expressed using the inverse of the function f above: X=Xnf−1(L⋆+16116+a⋆500)Y=Ynf−1(L⋆+16116)Z=Znf−1(L⋆+16116−b⋆200) where f−1(t)={t3if t>δ3δ2(t−429)otherwise
CIELAB_color_space
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted
Exponential_function
Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Function spaces generalizing finite-dimensional p norm spaces
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes
Lp_space
Correlation of a signal with a time-shifted copy of itself, as a function of shift
k,ℓ)=∑n,q,rxn,q,rx‾n−j,q−k,r−ℓ. When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is
Autocorrelation
Fourth standardized moment in statistics
Different measures of kurtosis can yield varying interpretations. The standard measure of a distribution's kurtosis, originating with Karl Pearson, is
Kurtosis
Set of rules defining correctly structured C++ program
defined in the standard as syntactic sugar for an unnamed function object. C++20 introduces support for coroutines, which are stackless functions whose execution
C++_syntax
Statistical model for a binary dependent variable
regression can begin with an explanation of the standard logistic function. The logistic function is a sigmoid function, which takes any real input t, and outputs
Logistic_regression
Branch of mathematics
of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called
Calculus
Gradient of the likelihood function
derivatives) of log L ( θ ; x ) {\displaystyle \log {\mathcal {L}}(\theta ;x)} , the natural logarithm of the likelihood function, with respect to an
Informant_function
Graphical programming language
the five languages defined by IEC 61131-3 standard. The SFC standard is defined as Preparation of function charts for control systems, and was based on
Sequential_function_chart
Input/output functionality in the C programming language
language provides many standard library functions for file input and output. These functions make up the bulk of the C standard library header <stdio.h>
C_file_input/output
Second-order partial differential equation
spherical harmonic functions multiplied by the appropriate scale factor rℓ, f ( r , θ , φ ) = ∑ ℓ = 0 ∞ ∑ m = − ℓ ℓ f ℓ m r ℓ Y ℓ m ( θ , φ ) , {\displaystyle
Laplace's_equation
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Monetary system based on the value of gold
A gold standard is a monetary system in which the standard economic unit of account is defined by a fixed quantity of gold. The gold standard was the basis
Gold_standard
Official keyboard layout of Canada
government standard for the Quebec public service SGQRI-001 requires the use of standardized pictograms following the ISO 9995-7 standard or function key labelling
CSA_keyboard
Statistical property
The standard error (SE) of a statistic is the standard deviation of its sampling distribution. It is the square root of the variance of an estimator of
Standard_error
Transcendental single-variable function
tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred
Clausen_function
Integral transform useful in probability theory, physics, and engineering
transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle
Laplace_transform
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STANDARD L-FUNCTION
STANDARD L-FUNCTION
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STANDARD L-FUNCTION
STANDARD L-FUNCTION
STANDARD L-FUNCTION
STANDARD L-FUNCTION
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