Automorphic forms and related geometry : assessing the legecy of I. I. Piatetski-Shapiro : Conference on Automorphic Forms and Related Geometry : April 23-27, 2012, Yale University, New Haven, CT / James W. Cogdell, Freydoon Shahidi, David Soudry, editors.

Format:

Book

Conference/Event

Contributor:

Cogdell, James W., 1953- editor.

Shahidi, Freydoon, editor.

Soudry, David, 1956- editor.

Conference Name:

Automorphic Forms and Related Geometry (Conference) (2012 : Yale University)

Automorphic Forms and Related Geometry (Conference)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 614

Contemporary mathematics, 1098-3627 ; 614 0271-4132

Language:

English

Subjects (All):

Pi︠a︡tet︠s︡kiĭ-Shapiro, I. I. (Ilʹi︠a︡ Iosifovich), 1929-2009.

Pi︠a︡tet︠s︡kiĭ-Shapiro, I. I.

Automorphic forms--Congresses.

Automorphic forms.

L-functions--Congresses.

L-functions.

Forms (Mathematics)--Congresses.

Forms (Mathematics).

Geometry--Congresses.

Geometry.

Physical Description:

1 online resource (454 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

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 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 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.

Contents:

References

A -adic integral for the reciprocal of -functions

1. Introduction and Motivation

2. Mazur's measure and its real analytic interpretation

3. Fourier coefficients of classical Eisenstein series

4. Proof of \thmref{th1}

Acknowledgements

References

Harmonic analysis on symmetric spaces as complex analysis

1. Horospherical reduction of complex symmetric spaces (geometrical picture)

2. Horospherical reduction of complex symmetric spaces (analytic construction of intertwining operators)

3. Dual horospherical Cauchy transform

4. Cauchy formula on complex symmetric spaces

5. Horospherical duality for real symmetric spaces. Compact spaces

6. Horospherical duality for complex crowns of symmetric spaces

7. Tube Stein manifolds on causal symmetric spaces

Testing rationality of coherent cohomology of Shimura varieties

Introduction

1. Restrictions of discrete series representations and global consequences

2. Restrictions of minimal types

3. Coherent cohomology of unitary group Shimura varieties

4. Gross-Prasad periods as cup products

6. The case =3, = =2

7. The case = = =2

8. The case =1

9. Application to holomorphic unitary representations

Mellin Transform of Whittaker functions

1. Introduction

2. Proof of the Theorem

Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

2. Arthur Parametrization of Discrete Spectrum

3. Endoscopy Structures for Classical Groups

4. Fourier Coefficients and Nilpotent Orbits

5. Constructions of the Automorphic Kernel Functions

6. Automorphic Descents and Automorphic Forms of Simple Type

An inductive formula for -factors

On a new functional equation for local integrals

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

On a certain sum of automorphic -functions

Analytic constructions of -adic -functions and Eisenstein series

On stability of root numbers

CAP forms, Eisenstein series, and some arithmetic applications

Automorphic descent: an outgrowth from Piatetski-Shapiro’s vision

On the singularities of branch curves of 3 surfaces and applications.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1658-1