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Advanced Analytic Number Theory: L-Functions
 
Carlos Julio Moreno The City University of New York (CUNY), New York, NY
Front Cover for Advanced Analytic Number Theory: L-Functions
Available Formats:
Softcover ISBN: 978-0-8218-4266-9
Product Code: SURV/115.S
List Price: $90.00
MAA Member Price: $81.00
AMS Member Price: $72.00
Electronic ISBN: 978-1-4704-1342-2
Product Code: SURV/115.S.E
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $67.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Front Cover for Advanced Analytic Number Theory: L-Functions
Click above image for expanded view
Advanced Analytic Number Theory: L-Functions
Carlos Julio Moreno The City University of New York (CUNY), New York, NY
Available Formats:
Softcover ISBN:  978-0-8218-4266-9
Product Code:  SURV/115.S
List Price: $90.00
MAA Member Price: $81.00
AMS Member Price: $72.00
Electronic ISBN:  978-1-4704-1342-2
Product Code:  SURV/115.S.E
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $67.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1152005; 291 pp
    MSC: Primary 11; 22;

    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.

    Readership

    Graduate students and research mathematicians interested in analytic number theory.

  • Table of Contents
     
     
    • Chapters
    • I. Hecke L-functions
    • II. Artin-Hecke L-functions
    • III. Analytic properties of L-functions
    • IV. The explicit formulas
    • V. Bounds on discriminants and conductors
    • VI. Non-vanishing theorems
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1152005; 291 pp
MSC: Primary 11; 22;

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.

Readership

Graduate students and research mathematicians interested in analytic number theory.

  • Chapters
  • I. Hecke L-functions
  • II. Artin-Hecke L-functions
  • III. Analytic properties of L-functions
  • IV. The explicit formulas
  • V. Bounds on discriminants and conductors
  • VI. Non-vanishing theorems
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.