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Advanced Analytic Number Theory: L-Functions
Carlos Julio Moreno, The City University of New York (CUNY), NY

Mathematical Surveys and Monographs
2005; 291 pp; softcover
Volume: 115
ISBN-10: 0-8218-4266-8
ISBN-13: 978-0-8218-4266-9
List Price: US$80
Member Price: US$64
Order Code: SURV/115.S
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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.


Graduate students and research mathematicians interested in analytic number theory.

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