# [PDF] Advanced Analytic Number Theory: L-Functions (Mathematical Surveys & Monographs) (Mathematical Surveys and Monographs)

#### ISBN: 0821842668

#### Category: Tutorial

Posted on 2018-01-20, by luongquocchinh.

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Author: Carlos Moreno | Publisher: American Mathematical Society | Category: Mathematics | Language: English | Page: 291 | ISBN: 0821842668 | ISBN13: 9780821842669 |

**Description:**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

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