In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula...

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...

conjecture Special values of L-functions Explicit formulae for L-functions Shimizu L-function Steuding, Jörn (June 2005). "An Introduction to the Theory of L-functions"...

Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical...

(1984) had proposed a set of far-reaching conjectures describing the special values of L-functions, i.e., the values of L-functions at integers. In very rough...

{r}{k}}\right).} Generalized Riemann hypothesis L-function Modularity theorem Artin conjecture Special values of L-functions Apostol 1976, Theorem 11.7 Davenport...

elliptic functions and approximately equal to 2.62205755. It also appears in evaluation of the gamma and beta function at certain rational values. The symbol...

special values of L-functions. The lower K-groups were discovered first, in the sense that adequate descriptions of these groups in terms of other algebraic...

adding and subtracting logarithmic values instead of multiplying and dividing very large values. It is often defined as l o g Γ ⁡ ( z ) = − γ z − log ⁡ z...

is used to formulate Beilinson conjectures on special values of L-functions. There is an extension of Deligne-cohomology defined for any symmetric spectrum...

conjectures for special values of L-functions in 1990. Bloch is a member of the U.S. National Academy of Sciences and a Fellow of the American Academy of Arts and...

function, such as Deligne's conjecture on special values of L-functions, the Beilinson conjecture, and the Bloch–Kato conjecture (on special values of...

intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions. Yuan is from Macheng, Huanggang, Hubei province, and graduated...

University of California, San Diego. His research interests are in algebraic number theory, and in particular, in special values of L-functions. The son of historian...

{\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}} where L {\displaystyle L} is the carrying capacity, the supremum of the values of the function; k {\displaystyle...

Real-valued functions of a real variable (commonly called real functions) and real-valued functions of several real variables are the main object of study...

In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems...

can analytically continue these functions to the n-dimensional complex space. The special values taken by these functions at positive integer arguments...

Deligne conjecture on special values of L-functions is a formulation of the hope for algebraicity of L(n) where L is an L-function and n is an integer in...

elliptic curves to special values of L-functions, which was developed with Bryan Birch during the first half of the 1960s with the help of machine computation...

quadratic form. It is a special case of a Hasse–Weil L-function. The natural definition of L(E, s) only converges for values of s in the complex plane...

elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as well as in the design of electronic...

sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given...

equal to L. The limit in Euclidean space is a direct generalization of limits to vector-valued functions. For example, we may consider a function f : S ×...

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...

rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic...

the two values y = W0(x) and y = W−1(x) if −⁠1/e⁠ ≤ x < 0. The Lambert W function's branches cannot be expressed in terms of elementary functions. It is...

functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions...

is a particular Dirichlet L-function, the L-function for the alternating character of period four. The Dirichlet beta function is defined as β ( s ) = ∑...

mathematics, a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values (its...