Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Advanced Analytic Number Theory: L-Functions
 
Carlos Julio Moreno The City University of New York (CUNY), New York, NY
Advanced Analytic Number Theory: L-Functions
Softcover ISBN:  978-0-8218-4266-9
Product Code:  SURV/115.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 28, 2024
eBook ISBN:  978-1-4704-1342-2
Product Code:  SURV/115.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4266-9
eBook: ISBN:  978-1-4704-1342-2
Product Code:  SURV/115.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 28, 2024
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
Softcover ISBN:  978-0-8218-4266-9
Product Code:  SURV/115.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 28, 2024
eBook ISBN:  978-1-4704-1342-2
Product Code:  SURV/115.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4266-9
eBook ISBN:  978-1-4704-1342-2
Product Code:  SURV/115.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 28, 2024
  • 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 publishers of book reviews
    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 publishers of book reviews
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.