Advanced Analytic Number Theory: L-Functions (Mathematical Surveys and Monographs No. 115)
By: Carlos Moreno (author)Paperback
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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.
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
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- ID: 9780821842669
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