Contributions to Automorphic Forms Geometry and Number Theory

by Hida, Haruzo; Ramakrishnan, Dinakar; Shahidi, Freydoon

ISBN13: 9780801878602

ISBN10: 0801878608

Format: Hardcover

Pub. Date: 2004-02-04

Publisher(s): Johns Hopkins Univ Pr

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Summary

In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Herve Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vigneras, Jean-Loup Waldspurger.

Author Biography

Haruzo Hida is a professor of mathematics at UCLA. Dinakar Ramakrishnan is a professor of mathematics at California Institute of Technology. Freydoon Shahidi is Distinguished Professor of Mathematics at Purdue University.

Preface	vii
Joe Shalika and the Fine Hall Days, 1968-1971, by Stephen Gelbart	ix
1 Joseph A. Shalika, Representation of the two by two unimodular group over local fields	1	(38)
2 Jeffrey Adams, Theta-10	39	(18)
3 Jeffrey D. Adler, Lawrence Corwin, and Paul J. Sally, Jr., Discrete series characters of division algebras and GLn over a p-adic field	57	(8)
4 James Arthur, Automorphic representations of GSp(4)	65	(18)
5 Don Blasius, Elliptic curves, Hilbert modular, forms, and the Hodge conjecture	83	(22)
6 Siegfried Böcherer, Masaaki Furusawa, and Rainer Schulze-Pillot, On the global Gross-Prasad conjecture for Yoshida liftings	105	(26)
7 Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein, Sums of twisted GL(3) automorphic L-functions	131	(32)
8 Bill Casselman, Harmonic analysis of the Schwartz space of γ \SL2(R)	163	(30)
9 Laurent Clozel and Emmanuel Ullmo, Equidistribution des points de Hecke	193	(62)
10 James W. Cogdell and Ilya I. Piatetski-Shapiro, Remarks on Rankin-Selberg convolutions	255	(24)
11 Benedict H. Gross and Joe Harris, On some geometric constructions related to theta characteristics	279	(34)
12 Thomas C. Hales, Can p-adic integrals be computed?	313	(18)
13 Michael Harris, Occult period invariants and critical values of the degree four L-function of GSp(4)	331	(24)
14 Michael Harris and Stephen S. Kudla, On a conjecture of Jacquet	355	(18)
15 Herve Jacquet, Integral representation of Whittaker functions	373	(48)
16 Herve Jacquet, Erez Lapid, and Stephen Rallis, A spectral identity for skew symmetric matrices	421	(36)
17 Dihua Jiang and David Soudry, Generic representations and local Langlands reciprocity law for p-adic SO2n+1	457	(64)
18 Nicholas M. Katz, Larsen's alternative, moments, and the monodromy of Lefschetz pencils	521	(40)
19 Henry H. Kim and Freydoon Shahidi, On the holomorphy of certain L: functions	561	(12)
20 Victor Kreiman and V. Lakshmibai, Richardson varieties in the Grassmannian	573	(26)
21 Philip Kutzko, Types and covers for SL(2)	599	(12)
22 Robert P. Langlands, Beyond endoscopy	611	(88)
23 Dipendra Prasad, An analogue of a conjecture of Mazur: A question in Diophantine approximation on tori	699	(12)
24 Dinakar Ramakrishnan, Existence of Ramanujan primes for GL(3)	711	(8)
25 Peter Sarnak, Nonvanishing of L -functions on R(s) = 1	719	(14)
26 Joseph A. Shalika, Ramin Takloo-Bighash, and Yuri Tschinkel, Rational points and automorphic forms	733	(10)
27 Joseph A. Shalika and Yuri Tschinkel, Height zeta functions of equivariant compactifications of the Heisenberg group	743	(30)
28 Marie-France Vignéras, On highest Whittaker models and integral structures	773	(30)
29 Jean-Loup Waldspurger, Représentations de réduction unipotente pour SO(2n+1): quelques conséquences d'un article de Lusztig	803