Advanced analytic number theory : L-functions
著者
書誌事項
Advanced analytic number theory : L-functions
（Mathematical surveys and monographs, v. 115）
American Mathematical Society, c2005
- : pbk
大学図書館所蔵 全43件
注記
Includes bibliographical references (p. 283-290) and index
内容説明・目次
内容説明
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.
目次
Hecke L-functions Artin-Hecke L-functions Analytic properties of L-functions The explicit formulas Bounds on discriminants and conductors Non-vanishing theorems The local theory of root numbers: A survey Bibliography Index.
「Nielsen BookData」 より