eBook ISBN:  9781470416584 
Product Code:  CONM/614.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470416584 
Product Code:  CONM/614.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 614; 2014; 441 ppMSC: Primary 11; 22; 14
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. PiatetskiShapiro, held from April 23–27, 2012, at Yale University, New Haven, CT.
Ilya I. PiatetskiShapiro, 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 PiatetskiShapiro's lifetime by him and a substantial group of his coworkers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected PiatetskiShapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global \(L\)functions and their periods; \(p\)adic \(L\)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 PiatetskiShapiro'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 PiatetskiShapiro.
ReadershipGraduate students and research mathematicians interested in automorphic forms, number theory, representation theory, and geometry.

Table of Contents

Articles

James Arthur — On parameters for the group $SO(2n)$

J. W. Cogdell — PiatetskiShapiro’s Work on Converse Theorems

Stephen Gelbart, Stephen D. Miller, Alexei Panchishkin and Freydoon Shahidi — A $p$adic integral for the reciprocal of $L$functions

Simon Gindikin — Harmonic analysis on symmetric spaces as complex analysis

Michael Harris — Testing rationality of coherent cohomology of Shimura varieties

Haruzo Hida — Hecke fields of Hilbert modular analytic families

Roger Howe and Soo Teck Lee — Structure of holomorphic unitary representations: the case of $\mathbf {U_{2,2}}$

Hervé Jacquet — Mellin Transform of Whittaker functions

Dihua Jiang — Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

JuLee Kim — An inductive formula for $\varepsilon $factors

Erez Lapid and Zhengyu Mao — On a new functional equation for local integrals

Colette Mœglin — Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands

Ngô Bao Châu — On a certain sum of automorphic $L$functions

Alexei Panchishkin — Analytic constructions of $p$adic $L$functions and Eisenstein series

J. W. Cogdell, F. Shahidi and T.L. Tsai — On stability of root numbers

Christopher Skinner — CAP forms, Eisenstein series, and some arithmetic applications

David Soudry — Automorphic descent: an outgrowth from PiatetskiShapiro’s vision

Michael Friedman and Mina Teicher — On the singularities of branch curves of $K3$ surfaces and applications


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This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. PiatetskiShapiro, held from April 23–27, 2012, at Yale University, New Haven, CT.
Ilya I. PiatetskiShapiro, 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 PiatetskiShapiro's lifetime by him and a substantial group of his coworkers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected PiatetskiShapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global \(L\)functions and their periods; \(p\)adic \(L\)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 PiatetskiShapiro'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 PiatetskiShapiro.
Graduate students and research mathematicians interested in automorphic forms, number theory, representation theory, and geometry.

Articles

James Arthur — On parameters for the group $SO(2n)$

J. W. Cogdell — PiatetskiShapiro’s Work on Converse Theorems

Stephen Gelbart, Stephen D. Miller, Alexei Panchishkin and Freydoon Shahidi — A $p$adic integral for the reciprocal of $L$functions

Simon Gindikin — Harmonic analysis on symmetric spaces as complex analysis

Michael Harris — Testing rationality of coherent cohomology of Shimura varieties

Haruzo Hida — Hecke fields of Hilbert modular analytic families

Roger Howe and Soo Teck Lee — Structure of holomorphic unitary representations: the case of $\mathbf {U_{2,2}}$

Hervé Jacquet — Mellin Transform of Whittaker functions

Dihua Jiang — Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

JuLee Kim — An inductive formula for $\varepsilon $factors

Erez Lapid and Zhengyu Mao — On a new functional equation for local integrals

Colette Mœglin — Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands

Ngô Bao Châu — On a certain sum of automorphic $L$functions

Alexei Panchishkin — Analytic constructions of $p$adic $L$functions and Eisenstein series

J. W. Cogdell, F. Shahidi and T.L. Tsai — On stability of root numbers

Christopher Skinner — CAP forms, Eisenstein series, and some arithmetic applications

David Soudry — Automorphic descent: an outgrowth from PiatetskiShapiro’s vision

Michael Friedman and Mina Teicher — On the singularities of branch curves of $K3$ surfaces and applications