Advanced Analytic Number Theory: L-functions

Erscheinungsjahr 2005
ISBN: 978-0-8218-4266-9
Verlag: American Mathematical Society

Buch, Englisch, Band 115, 291 Seiten, Gewicht: 548 g

Reihe: Mathematical Surveys and Monographs

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.

Zielgruppe

Graduate students and research mathematicians interested in analytic number theory

Autoren/Hrsg.

Moreno, Carlos

Moreno, Carlos Julio

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

Carlos Julio Moreno, The City University of New York (CUNY), NY