Advanced analytic number theory : L-functions

著者

• Moreno, Carlos J.

書誌事項

Advanced analytic number theory : L-functions

Carlos Julio Moreno

（Mathematical surveys and monographs, v. 115）

American Mathematical Society, c2005

• : pbk

注記

Includes bibliographical references (p. 283-290) and index

内容説明・目次

巻冊次

ISBN 9780821836415

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.

巻冊次

: pbk ISBN 9780821842669

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
• 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

詳細情報

• NII書誌ID(NCID): BA71975139
• ISBN:
  • 0821836412
  • 0821842668
• LCCN: 2005041057
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xx, 291 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA246
  • DC22 : 512.7/3
• 件名:
  • LCSH : L-functions
  • LCSH : Algebraic number theory
  • LCSH : Lie groups
• 親書誌ID:
  • BA00134419