Automorphic Forms And L Functions I

Author : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 65 pages
File Size : 54,7 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 9781139456203

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Automorphic Forms and L-Functions for the Group GL(n,R) by Dorian Goldfeld Pdf

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.

Author : Armand Borel,W. Casselman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 47,6 Mb
Release : 1979-06-30
Category : Mathematics
ISBN : 9780821814376

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Automorphic Forms, Representations and $L$-Functions by Armand Borel,W. Casselman,American Mathematical Society Pdf

Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions

Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 51,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540390558

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Automorphic Forms on GL (3,TR) by D. Bump Pdf

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 50,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849897

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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 : Dorian Goldfeld,Joseph Hundley
Publisher : Cambridge University Press
Page : 209 pages
File Size : 41,7 Mb
Release : 2011-04-21
Category : Mathematics
ISBN : 9781139503082

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Automorphic Representations and L-Functions for the General Linear Group: Volume 2 by Dorian Goldfeld,Joseph Hundley Pdf

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

Author : Stephen Gelbart,Ilya Piatetski-Shapiro,Stephen Rallis
Publisher : Springer
Page : 158 pages
File Size : 47,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478805

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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 : Alvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 53,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852422

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Elliptic Curves, Modular Forms, and Their L-functions by Alvaro Lozano-Robledo Pdf

Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

Author : Stephen Gelbart,Freydoon Shahidi
Publisher : Academic Press
Page : 142 pages
File Size : 49,6 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483261034

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Analytic Properties of Automorphic L-Functions by Stephen Gelbart,Freydoon Shahidi Pdf

Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products . This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 44,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376125

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Automorphic Forms on GL (2) by H. Jacquet Pdf

Author : David Ginzburg
Publisher : American Mathematical Soc.
Page : 339 pages
File Size : 54,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847084

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Automorphic Forms and $L$-functions II by David Ginzburg Pdf

Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Author : Jan Hendrik Bruinier,Winfried Kohnen
Publisher : Springer
Page : 366 pages
File Size : 55,8 Mb
Release : 2018-02-22
Category : Mathematics
ISBN : 9783319697123

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L-Functions and Automorphic Forms by Jan Hendrik Bruinier,Winfried Kohnen Pdf

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Author : David Ginzburg,Erez Lapid,David Soudry
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847060

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Automorphic Forms and $L$-functions I by David Ginzburg,Erez Lapid,David Soudry Pdf

Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 54,6 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9781447144359

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Automorphic Forms by Anton Deitmar Pdf

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.

Author : James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 45,5 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 082187179X

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Lectures on Automorphic L-functions by James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty Pdf

James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 54,5 Mb
Release : 2007-10-10
Category : Mathematics
ISBN : 9780817646462

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.