ADVANCED ANALYTIC NUMBER THEORY by Carlos Julio Moreno ( 9780821842669 )

Item Details

Title:

ADVANCED ANALYTIC NUMBER THEORY
L-FUNCTIONS

By:

Format:

Paperback

List price:	£113.00
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ISBN 10:

0821842668

ISBN 13:

9780821842669

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 January, 2005

Series:

Mathematical Surveys and Monographs No. 115

Pages:

291

Synopsis:

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations.The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Publication:

Imprint:

Chelsea Publishing

Returns:

Returnable

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