Elementary Theory Of L Functions And Eisenstein Series

Author : Haruzo Hida
Publisher : Cambridge University Press
Page : 404 pages
File Size : 44,8 Mb
Release : 1993-02-11
Category : Mathematics
ISBN : 0521435692

Get Book

Elementary Theory of L-functions and Eisenstein Series by Haruzo Hida Pdf

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 49,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849897

Get Book

Eisenstein Series and Automorphic $L$-Functions by Freydoon Shahidi Pdf

This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 52,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821842669

Get Book

Advanced Analytic Number Theory: L-Functions by Carlos J. Moreno Pdf

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.

Author : Colette Moeglin,J. L. Waldspurger
Publisher : Cambridge University Press
Page : 382 pages
File Size : 41,5 Mb
Release : 1995-11-02
Category : Mathematics
ISBN : 0521418933

Get Book

Spectral Decomposition and Eisenstein Series by Colette Moeglin,J. L. Waldspurger Pdf

A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.

Author : Stephen Gelbart,Ilya Piatetski-Shapiro,Stephen Rallis
Publisher : Springer
Page : 158 pages
File Size : 53,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478805

Get Book

Explicit Constructions of Automorphic L-Functions by Stephen Gelbart,Ilya Piatetski-Shapiro,Stephen Rallis Pdf

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.

Author : Michel Courtieu,Alexei A. Panchishkin
Publisher : Springer
Page : 204 pages
File Size : 43,8 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540451785

Get Book

Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms by Michel Courtieu,Alexei A. Panchishkin Pdf

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.

Author : Stephen S. Gelbart,Freydoon Shahidi
Publisher : Unknown
Page : 152 pages
File Size : 48,9 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B5008733

Get Book

Analytic Properties of Automorphic L-functions by Stephen S. Gelbart,Freydoon Shahidi Pdf

Analytic Properties of Automorphic L-Functions.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 44,5 Mb
Release : 2007-08-06
Category : Mathematics
ISBN : 9780387724744

Get Book

Elementary Dirichlet Series and Modular Forms by Goro Shimura Pdf

A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

Author : David Loeffler,Sarah Livia Zerbes
Publisher : Springer
Page : 492 pages
File Size : 44,5 Mb
Release : 2017-01-15
Category : Mathematics
ISBN : 9783319450322

Get Book

Elliptic Curves, Modular Forms and Iwasawa Theory by David Loeffler,Sarah Livia Zerbes Pdf

Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.

Author : Fred Diamond,Payman L. Kassaei,Minhyong Kim
Publisher : Cambridge University Press
Page : 385 pages
File Size : 42,9 Mb
Release : 2014-10-16
Category : Mathematics
ISBN : 9781107691926

Get Book

Automorphic Forms and Galois Representations by Fred Diamond,Payman L. Kassaei,Minhyong Kim Pdf

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Author : Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura
Publisher : Springer Nature
Page : 419 pages
File Size : 42,9 Mb
Release : 2024-02-03
Category : Mathematics
ISBN : 9789819909100

Get Book

The Theory of Zeta-Functions of Root Systems by Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura Pdf

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.

Author : Robert P. Langlands
Publisher : Springer
Page : 344 pages
File Size : 49,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540380702

Get Book

On the Functional Equations Satisfied by Eisenstein Series by Robert P. Langlands Pdf

Author : Joël Bellaïche
Publisher : Springer Nature
Page : 319 pages
File Size : 48,5 Mb
Release : 2021-08-11
Category : Mathematics
ISBN : 9783030772635

Get Book

The Eigenbook by Joël Bellaïche Pdf

​This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.

Author : Thanasis Bouganis,Otmar Venjakob
Publisher : Springer
Page : 483 pages
File Size : 41,8 Mb
Release : 2014-12-08
Category : Mathematics
ISBN : 9783642552458

Get Book

Iwasawa Theory 2012 by Thanasis Bouganis,Otmar Venjakob Pdf

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).

Author : Wenpeng Zhang,Yoshio Tanigawa
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 40,5 Mb
Release : 2006-06-05
Category : Mathematics
ISBN : 9780387308296

Get Book

Number Theory by Wenpeng Zhang,Yoshio Tanigawa Pdf

This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.