automorphic function

См. также в других словарях:

• Automorphic form — In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms. It is in terms of a Lie group G, to generalise the groups SL2(R) or PSL2 (R) of… …   Wikipedia

• Automorphic factor — In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms. The general case, for general groups, is reviewed in the article factor of automorphy .… …   Wikipedia

• Artin L-function — In mathematics, an Artin L function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G . These functions were introduced in the 1923 by Emil Artin, in connection with his research into class field theory.… …   Wikipedia

• Motivic L-function — In mathematics, motivic L functions are a generalization of Hasse–Weil L functions to general motives over global fields. The local L factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v… …   Wikipedia

• Selberg zeta function — The Selberg zeta function was introduced by Atle Selberg in the 1950s. It is analogous to the famous Riemann zeta function :zeta(s) = prod {pinmathbb{P frac{1}{1 p^{ s where mathbb{P} is the set of prime numbers. The Selberg zeta function uses… …   Wikipedia

• L-function — The theory of L functions has become a very substantial, and still largely conjectural, part of contemporary number theory. In it, broad generalisations of the Riemann zeta function and the L series for a Dirichlet character are constructed, and… …   Wikipedia

• Hasse-Weil zeta function — In mathematics, the Hasse Weil zeta function attached to an algebraic variety V defined over a number field K is one of the two most important types of L function. Such L functions are called global , in that they are defined as Euler products in …   Wikipedia

• Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… …   Wikipedia

• Dedekind zeta function — In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function which is obtained by specializing to the case where K is the rational numbers Q. In particular,… …   Wikipedia

• Dirichlet L-function — In mathematics, a Dirichlet L series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1. By analytic continuation, this function can be extended to a meromorphic function on the whole… …   Wikipedia

• Functional equation (L-function) — In mathematics, the L functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations. There is an elaborate theory of what these equations should be, much of which …   Wikipedia