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

[Book Description]

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.

[Table of Contents] 

On parameters for the group SO(2n)             1  (30)
          James Arthur
    Piatetski-Shapiro's work on converse           31 (22)
    theorems
          J. W. Cogdell
    A p-adic integral for the reciprocal of        53 (16)
    L-functions
          Stephen Gelbart
          Stephen D. Miller
          Alexei Panchishkin
          Freydoon Shahidi
    Harmonic analysis on symmetric spaces as       69 (12)
    complex analysis
          Simon Gindikin
    Testing rationality of coherent cohomology     81 (16)
    of Shimura varieties
          Michael Harris
    Hecke fields of Hilbert modular analytic       97 (42)
    families
          Haruzo Hida
    Structure of holomorphic unitary               139(32)
    representations: The case of U2,2
          Roger Howe
          Soo Teck Lee
    Mellin transform of Whittaker functions        171(8)
          Herve Jacquet
    Automorphic integral transforms for            179(64)
    classical groups I: Endoscopy
    correspondences
          Dihua Jiang
    An inductive formula for e-factors             243(18)
          Ju-Lee Kim
    On a new functional equation for local         261(34)
    integrals
          Erez Lapid
          Zhengyu Mao
    Paquets stables des series discretes           295(42)
    accessibles par endoscopie tordue; leur
    parametre de Langlands
          Colette M$$glin
    On a certain sum of autmorphic L-functions     337(8)
          Ngô Bao Châu
    Analytic constructions of p-adic               345(30)
    L-functions and Eisenstein series
          Alexei Panchishkin
    On stability of root numbers                   375(12)
          J. W. Cogdell
          F. Shahidi
          T.-L. Tsai
    CAP forms, Eisenstein series, and some         387(20)
    arithmetic applications
          Christopher Skinner
    Automorphic descent: An outgrowth from         407(26)
    Piatetski-Shapiro's vision
          David Soudry
    On the singularities of branch curves of K3    433
    surfaces and applications
          Michael Friedman
          Mina Teicher