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.
J. Arthur - On parameters for the group SO(2n)
J. W. Cogdell - Piateski-Shapiro's work on converse theorems
S. Gelbart, S. D. Miller, A. Panchishkin, and F. Shahidi - A p -adic integral
for the reciprocal of L -functions
S. Gindikin - Harmonic analysis on symmetric spaces as complex analysis
M. Harris - Testing rationality of coherent cohomology of Shimura varieties
H. Hida - Hecke fields of Hilbert modular analytic families
R. Howe and S. T. Lee - Structure of holomorphic unitary representations: The
case of U 2,2
H. Jacquet - Mellin transform of Whittaker functions
D. Jiang - Automorphic integral transforms for classical groups I: Endoscopy
correspondences
J.-L. Kim - An inductive formula for ? -factors
E. Lapid and Z. Mao - On a new functional equation for local integrals
C. Mglin - Paquets stables des séries discrètes accessibles par endoscopie
tordue; leur paramètre de Langlands
N. B. Châu - On a certain sum of automorphic L -functions
A. 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
C. Skinner - Cap forms, Eisenstein series, and some arithmetic applications
D. Soudry - Automorphic descent: An outgrowth from Piatetski-Shapiro's
vision
M. Friedman and M. Teicher - On the singularities of branch curves of K3
surfaces and applications
James W. Cogdell, Ohio State University, Columbus, OH.
Freydoon Shahidi, Purdue University, West Lafayette, IN.
David Soudry, Tel Aviv University, Israel.
Lisainfo e-raamatute kohta