Automorphic forms and related geometry: assessing the legecy of I.I. Piatetski-Shapiro / [edited by] James W. Cogdell, Freydoon Shahidi and David Soudry.

Includes bibliographical references.

On parameters for the group SO(2n)
Piateski-Shapiro's work on converse theorems
A p -adic integral for the reciprocal of L -functions
Harmonic analysis on symmetric spaces as complex analysis Testing rationality of coherent cohomology of Shimura varieties Hecke fields of Hilbert modular analytic families
Structure of holomorphic unitary representations: The case of U 2,2
Mellin transform of Whittaker functions
Automorphic integral transforms for classical groups I: Endoscopy correspondences
An inductive formula for e-factors
On a new functional equation for local integrals
Paquets stables des series discretes accessibles par endoscopie tordue; leur parametre de Langlands
On a certain sum of automorphic L -functions
Analytic constructions of p -adic L -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 K3 surfaces and applications.

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.