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Softcover ISBN:  9780821842669 
Product Code:  SURV/115.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413422 
Product Code:  SURV/115.S.E 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821842669 
eBook ISBN:  9781470413422 
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Book DetailsMathematical Surveys and MonographsVolume: 115; 2005; 291 ppMSC: Primary 11; 22;
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of Lfunctions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, Lfunctions 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 Lfunctions: the ArtinHecke Lfunctions associated to finitedimensional representations of Weil groups and to automorphic Lfunctions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and nonvanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of ArtinHecke and automorphic Lfunctions is also given.
The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of Lfunctions 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.ReadershipGraduate students and research mathematicians interested in analytic number theory.

Table of Contents

Chapters

I. Hecke Lfunctions

II. ArtinHecke Lfunctions

III. Analytic properties of Lfunctions

IV. The explicit formulas

V. Bounds on discriminants and conductors

VI. Nonvanishing theorems


Additional Material

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Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of Lfunctions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, Lfunctions 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 Lfunctions: the ArtinHecke Lfunctions associated to finitedimensional representations of Weil groups and to automorphic Lfunctions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and nonvanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of ArtinHecke and automorphic Lfunctions is also given.
The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of Lfunctions 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.

Chapters

I. Hecke Lfunctions

II. ArtinHecke Lfunctions

III. Analytic properties of Lfunctions

IV. The explicit formulas

V. Bounds on discriminants and conductors

VI. Nonvanishing theorems