L Functions For The Orthogonal Group

Author : David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 49,8 Mb
Release : 1997
Category : Automorphic functions
ISBN : 9780821805435

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$L$ Functions for the Orthogonal Group by David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis Pdf

In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.

Author : Stephen Rallis
Publisher : Walter de Gruyter
Page : 442 pages
File Size : 55,8 Mb
Release : 2005
Category : Mathematics
ISBN : 3110179393

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Automorphic Representations, L-functions and Applications by Stephen Rallis Pdf

This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27-30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin-Selberg L-functions (Bump, Ginzburg-Jiang-Rallis, Lapid-Rallis) the relative trace formula (Jacquet, Mao-Rallis) automorphic representations (Gan-Gurevich, Ginzburg-Rallis-Soudry) representation theory of p-adic groups (Baruch, Kudla-Rallis, Moeglin, Cogdell-Piatetski-Shapiro-Shahidi) p-adic methods (Harris-Li-Skinner, Vigneras), and arithmetic applications (Chinta-Friedberg-Hoffstein). The survey articles by Bump, on the Rankin-Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.

Author : Mehmet Okan Tekman
Publisher : Unknown
Page : 102 pages
File Size : 53,9 Mb
Release : 1992
Category : Electronic
ISBN : MINN:31951D007544117

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Special Values of L-functions Attached to Holomorphic Cuspforms on Orthogonal Groups of Hermitian Type by Mehmet Okan Tekman Pdf

Author : Stephen Gelbart,Ilya Piatetski-Shapiro,Stephen Rallis
Publisher : Springer
Page : 158 pages
File Size : 41,5 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 : James W. Cogdell,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 454 pages
File Size : 46,8 Mb
Release : 2014-04-01
Category : Mathematics
ISBN : 9780821893944

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Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro by James W. Cogdell,Freydoon Shahidi,David Soudry Pdf

This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.

Author : Jan Hendrik Bruinier,Winfried Kohnen
Publisher : Springer
Page : 366 pages
File Size : 43,7 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 : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 65 pages
File Size : 43,6 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 : Dorian Goldfeld,Joseph Hundley
Publisher : Cambridge University Press
Page : 209 pages
File Size : 40,6 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 : James Arthur
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 50,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852040

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On Certain $L$-Functions by James Arthur Pdf

Illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their $L$-functions, and both local and global theory are addressed. Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of $p$-adic groups, Plancherel formula and its consequences, and the Gross-Prasad conjecture.

Author : J. Coates,Martin J. Taylor
Publisher : Cambridge University Press
Page : 404 pages
File Size : 40,9 Mb
Release : 1991-02-22
Category : Mathematics
ISBN : 9780521386197

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L-Functions and Arithmetic by J. Coates,Martin J. Taylor Pdf

Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.

Author : Yu. I. Manin,Alexei A. Panchishkin
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 51,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662080054

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Number Theory I by Yu. I. Manin,Alexei A. Panchishkin Pdf

A unified survey of both the status quo and the continuing trends of various branches of number theory. Motivated by elementary problems, the authors present todays most significant results and methods. Topics covered include non-Abelian generalisations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. The book is rounded off with an overview of the major conjectures, most of which are based on analogies between functions and numbers, and on connections with other branches of mathematics such as analysis, representation theory, geometry and algebraic topology.

Author : Alexei A. Panchishkin
Publisher : Springer
Page : 167 pages
File Size : 47,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662215418

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Non-Archimedean L-Functions by Alexei A. Panchishkin Pdf

1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>

Author : Dorian Goldfeld,Joseph Hundley
Publisher : Cambridge University Press
Page : 571 pages
File Size : 51,6 Mb
Release : 2011-04-21
Category : Mathematics
ISBN : 9781139500135

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Automorphic Representations and L-Functions for the General Linear Group: Volume 1 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 : Freydoon Shahidi
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 50,9 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 : Dihua Jiang,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 42,8 Mb
Release : 2016-04-29
Category : Automorphic forms
ISBN : 9781470417093

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Advances in the Theory of Automorphic Forms and Their $L$-functions by Dihua Jiang,Freydoon Shahidi,David Soudry Pdf

This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their L-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna. The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their L-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of p-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, L-functions for classical groups, special values of L-functions, Howe duality, subconvexity for L-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on L-functions, nodal sets and geometry.