James W. Cogdell's Books

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

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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

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

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Page Count

300

Publisher

American Mathematical Soc.

ISBN 10

082187179X

ISBN 13

9780821871799

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro

By: James W. Cogdell,Freydoon Shahidi,David Soudry

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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

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.

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Page Count

454

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821893947

ISBN 13

9780821893944

The Arithmetic and Spectral Analysis of Poincaré Series

By: James W. Cogdell,Iiya Piatetski-Shapiro

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The Arithmetic and Spectral Analysis of Poincaré Series

By: James W. Cogdell,Iiya Piatetski-Shapiro

The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation. This book will be a valuable resource for students of mathematics.

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Page Count

190

Publisher

Academic Press

Published Date

ISBN 10

1483266176

ISBN 13

9781483266176

Forty Years' Familiar Letters of James W. Alexander, D.D., Constituting, with Notes, a Memoir of His Life:

By: James W. Alexander,John Hall

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Forty Years' Familiar Letters of James W. Alexander, D.D., Constituting, with Notes, a Memoir of His Life:

By: James W. Alexander,John Hall

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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Page Count

430

Publisher

Palala Press

Published Date

ISBN 10

1379274818

ISBN 13

9781379274810

Book's by James W. Cogdell

Lectures on Automorphic L-functions

Lectures on Automorphic L-functions

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro

The Arithmetic and Spectral Analysis of Poincaré Series

The Arithmetic and Spectral Analysis of Poincaré Series

Forty Years' Familiar Letters of James W. Alexander, D.D., Constituting, with Notes, a Memoir of His Life:

Forty Years' Familiar Letters of James W. Alexander, D.D., Constituting, with Notes, a Memoir of His Life:

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