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CONTEMPORARYMATHEMATICS
488
Automorphic Forms and L-functions I. Global Aspects
A Workshop in Honor of Steve Gelbart on the Occasion of his Sixtieth Birthday
May 15–19, 2006 Rehovot and Tel Aviv, Israel
David Ginzburg Erez Lapid
David Soudry Editors
American Mathematical SocietyProvidence, Rhode Island
Bar-Ilan University Ramat Gam, Israel
Israel Mathematical Conference Proceedings
Automorphic Forms and L-functions I. Global Aspects
http://dx.doi.org/10.1090/conm/488
Steve Gelbart
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CONTEMPORARYMATHEMATICS
488
Automorphic Forms and L-functions I. Global Aspects
A Workshop in Honor of Steve Gelbart on the Occasion of His Sixtieth Birthday
May 15-19, 2006 Rehovot and Tel Aviv, Israel
David Ginzburg Erez Lapid
David Soudry Editors
Israel Mathematical Conference Proceedings
American Mathematical SocietyProvidence, Rhode Island
Bar-Ilan University Ramat Gam, Israel
Editorial Board of Contemporary Mathematics
Dennis DeTurck, managing editor
George Andrews Abel Klein Martin J. Strauss
Editorial Board of Israel Mathematical Conference Proceedings
Louis Rowen, Bar-Ilan University, managing editor
Z. Arad, Netanya Academic College M. Katz, Bar-Ilan UniversityJ. Bernstein, Tel-Aviv University B. Pinchuk, Netanya Academic CollegeH. Furstenberg, Hebrew University S. Shnider, Bar-Ilan UniversityS. Gelbart, Weizmann Institute L. Small, University of California
at San DiegoV. Gol′dshtein, Ben-Gurion University L. Zalcman, Bar-Ilan University
Miriam Beller, Technical Editor
2000 Mathematics Subject Classification. Primary 11F70, 11F67; Secondary 11F72,11F27, 11F33, 11F75, 11F80.
Photo courtesy of David Soudry.
Library of Congress Cataloging-in-Publication Data
Automorphic forms and L-functions : proceedings of a workshop in honor of Steve Gelbart onthe occasion of his sixtieth birthday : May 15–19, 2006, Rehovot and Tel Aviv, Israel / DavidGinzburg, Erez Lapid, David Soudry, editors.
v. cm. — (Contemporary mathematics ; v. 488–489) (Israel mathematical conference pro-ceedings)
Includes bibliographical references.Contents: 1. Global aspects — 2. Local aspects.ISBN 978-0-8218-4706-0 (alk. paper) — ISBN 978-0-8218-4708-4 (alk. paper)1. Automorphic functions—Congresses. 2. L-functions—Congresses. 3. Automorphic forms—
Congresses. I. Gelbart, Stephen S., 1946– II. Ginzburg, David, 1958– III. Lapid, Erez, 1971–IV. Soudry, David, 1956–
QA353.A9A928 2006515′.9—dc22 2009000412
Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction byservices that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for generaldistribution, for advertising or promotional purposes, or for resale. Requests for permission forcommercial use of material should be addressed to the Managing Editor, IMCP, Department ofMathematics, Bar-Ilan University, Ramat-Gan, 52900 Israel. Requests can also be made by emailto rowen@macs.biu.ac.il.
Excluded from these provisions is material in articles for which the author holds copyright. Insuch cases, requests for permission to use or reprint should be addressed directly to the author(s).(Copyright ownership is indicated in the notice in the lower right-hand corner of the first page ofeach article.)
c© 2009 by Bar-Ilan University. Printed in the United States of America.©∞ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 14 13 12 11 10 09
ContentsI: Global Aspects
II. Local Aspects vii
Preface ix
Bibliography of Stephen S. Gelbart xi
Conference Program xvii
List of Participants xix
Report on the Trace Formula
James Arthur 1
L-functions for Um ×RE/F GLn
(n ≤ [m
2
])Asher Ben-Artzi and David Soudry 13
Gauss Sum Combinatorics and Metaplectic Eisenstein Series
Ben Brubaker, Daniel Bump, and Solomon Friedberg 61
On Partial Poincare Series
J. W. Cogdell and I. I. Piatetski-Shapiro 83
Restrictions of Saito-Kurokawa Representations
Wee Teck Gan and Nadya Gurevich (with an Appendix by GordanSavin) 95
Models for Certain Residual Representations of Unitary Groups
David Ginzburg, Dihua Jiang, and Stephen Rallis 125
Crown Theory for the Upper Half Plane
Bernhard Krotz 147
Unitary Periods and Jacquet’s Relative Trace Formula
Omer Offen 183
Remarks on the Symmetric Powers of Cusp Forms on GL(2)
Dinakar Ramakrishnan 237
The Cohomological Approach to Cuspidal Automorphic Representations
Joachim Schwermer 257
v
ContentsII: Local Aspects
Preface ix
Bibliography of Stephen S. Gelbart xi
Conference Program xvii
List of Participants xix
p-adic Interpolation of Triple L-functions: Analytic Aspects
Siegfried Bocherer and Alexei A. Panchishkin 1
Sur les Representations Modulo p de Groupes Reductifs p-adiques
Guy Henniart 41
Archimedean Rankin-Selberg Integrals
Herve Jacquet 57
On a Result of Venkatesh on Clozel’s Conjecture
Erez Lapid and Jonathan Rogawski 173
Paquets d’Arthur Discrets pour un Groupe Classique p-adique
Colette Mœglin 179
Complexity of Group Actions and Stability of Root Numbers
Freydoon Shahidi (with an Appendix by Wentang Kuo) 259
GL(n, C) and GL(n, R)
Marko Tadic 285
vii
Preface
The Workshop on Automorphic Forms and L-functions was held during the
beautiful spring days of May 15-19, 2006, in the Weizmann Institute of Science and
in Tel-Aviv University, Israel, in honor and celebration of the sixtieth birthday of
Steve Gelbart. This is the first of the two volumes which contain the proceedings
of this workshop.
The topics of the contributed articles represent leading themes of research in
automorphic forms today: the trace formula and its applications to functorial-
ity and representations of p-adic reductive groups; the relative trace formula and
periods of automorphic forms; Rankin-Selberg convolutions and L-functions; p-
adic L-functions. The articles in this volume concern mainly global aspects in
the study of automorphic forms, and those of the second volume (Contemporary
Mathematics, volume 489) concern mainly local aspects.
Steve Gelbart played a key role in the development of the theory of L-functions
of automorphic representations and its applications to the theta correspondence
and functoriality. The workshop and these two volumes are to acknowledge Steve
Gelbart’s achievements, impact and influence in automorphic forms and L-functions.
We are grateful to our sponsors for funding the workshop:
· The Israel Science Foundation (ISF)
· The Arthur and Rochelle Belfer Institute of Mathematics and Computer
Science
· The Maurice and Gabriella Goldschleger Conference Foundation at the
Weizmann Institute of Science
· Clay Mathematics Institute
· The European Research Network “Arithmetic Algebraic Geometry”
The Organizing Committee:
Vladimir Berkovich Erez Lapid
David Ellwood Peter Sarnak
David Ginzburg Freydoon Shahidi
Roger Howe David Soudry
ix
Bibliography of Stephen S. Gelbart
(1) Choquet, Gustave Lectures on Analysis. Vol. I: Integration and Topologi-cal Vector Spaces (edited by J. Marsden, T. Lance and S. Gelbart), W.A.
Benjamin, Inc., New York-Amsterdam, 1969 (with appendix).
(2) Choquet, Gustave Lectures on Analysis. Vol. II: Representation Theory(edited by J. Marsden, T. Lance and S. Gelbart), W. A. Benjamin, Inc.,
New York-Amsterdam, 1969.
(3) Choquet, Gustave, Lectures on Analysis. Vol. III: Infinite DimensionalMeasures and Problem Solutions (edited by J. Marsden, T. Lance and
S. Gelbart), W. A. Benjamin, Inc., New York-Amsterdam, 1969.
(4) Gelbart, Stephen S., Fourier analysis on GL(n, R), Proc. Nat. Acad.
Sci. U.S.A. 65 (1970), 14–18.
(5) Gelbart, Stephen S., Fourier Analysis on Matrix Space, Memoirs of the
American Mathematical Society, No. 108, American Mathematical Soci-
ety, Providence, R.I., 1971.
(6) Gelbart, Stephen S., Harmonics on Stiefel manifolds and generalizedHankel transforms, Bull. Amer. Math. Soc. 78 (1972), no. 3, 451–455.
(7) Gelbart, Stephen ,Holomorphic discrete series for the real symplectic groupInvent. Math. 19 (1973), 49–58.
(8) Gelbart, Stephen, Bessel functions, representation theory, and automor-phic functions, Harmonic Analysis on Homogeneous Spaces (Proc. Sym-
pos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972),
Amer. Math. Soc., Providence, R.I., 1973, pp. 343–345.
(9) Gelbart, Stephen, An example in the theory of automorphic forms,Harmonic Analysis on Homogeneous Spaces (Proc. Sympos. Pure Math.,
Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), Amer. Math.
Soc., Providence, R.I., 1973, pp. 437–439.
(10) Gelbart, Stephen, The decomposition of L2(Γ\G), Seminaire Choquet,
11e–12e annees (1971–1973), Initiation a l’analyse, Exp. No. 4, Secretariat
Mathmatique, Paris, 1973.
(11) Gelbart, Stephen, Introduction to the theory of group representations,Seminaire Choquet, 11e–12e annees (1971–1973), Initiation a l’analyse,
Exp. No. 3, Secretariat Mathmatique, Paris, 1973.
(12) Gelbart, Stephen S, A theory of Stiefel harmonics, Trans. Amer. Math.
Soc. 192 (1974), 29–50.
(13) Gelbart, Stephen S., Automorphic Forms on Adele Groups, Annals of
Mathematics Studies, No. 83, Princeton University Press, Princeton, N.J.,
University of Tokyo Press, Tokyo, 1975.
xi
xii BIBLIOGRAPHY OF STEPHEN S. GELBART
(14) Gelbart, Stephen; Sally, Paul, Intertwining operators and automorphicforms for the metaplectic group, Proc. Nat. Acad. Sci. U.S.A. 72 (1975),
1406–1410.
(15) Gelbart, Stephen, Automorphic Forms and Representations of Adele Groups,Lecture Notes in Representation Theory, Department of Mathematics,
University of Chicago, Chicago, Ill., 1975.
(16) Gelbart, Stephen; Jacquet, Herve, A relation between automorphic formson GL(2) and GL(3), Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 10,
3348–3350.
(17) Gelbart, Stephen S., Weil’s Representation and the Spectrum of the Meta-plectic Group, Lecture Notes in Mathematics, Vol. 530, Springer-Verlag,
Berlin-New York, 1976.
(18) Gelbart, Stephen, Elliptic curves and automorphic representations,Advances in Math. 21 (1976), no. 3, 235–292.
(19) Gelbart, Stephen, Automorphic forms and Artin’s conjecture, Modular
functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn.,
Bonn, 1976), Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977,
pp. 241–276.
(20) Gelbart, S.S.; Piatetski-Shapiro, I.I., Automorphic L-functions of half-integral weight, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 4, 1620–
1623.
(21) Gelbart, Stephen; Jacquet, Herve, A relation between automorphic rep-resentations of GL(2) and GL(3), Ann. Sci. Ecole Norm. Sup. (4) 11(1978), no. 4, 471–542.
(22) Gelbart, Stephen; Jacquet, Herve, Forms of GL(2) from the analytic pointof view, Automorphic Forms, Representations and L-functions (Proc. Sym-
pos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc.
Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979,
pp. 213–251.
(23) Gelbart, Stephen, Examples of dual reductive pairs, Automorphic Forms,
Representations and L-functions (Proc. Sympos. Pure Math., Oregon
State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math.,
XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 287–296.
(24) Gelbart, Stephen; Howe, Roger; Piatetski-Shapiro, Ilya, Uniqueness andexistence of Whittaker models for the metaplectic group, Israel J. Math.
34 (1979), no. 1-2, (1980), 21–37.
(25) Gelbart, Stephen; Piatetski-Shapiro, I.I., Distinguished representationsand modular forms of half-integral weight, Invent. Math. 59 (1980), no. 2,
145–188.
(26) Gelbart, S. S.; Knapp, A. W., Irreducible constituents of principal seriesof SLn(k), Duke Math. J. 48 (1981), no. 2, 313–326.
(27) Gelbart, S.; Piatetski-Shapiro, I., On Shimura’s correspondence for mod-ular forms of half-integral weight, Automorphic Forms, Representation
Theory and Arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies
in Math. 10, Tata Inst. Fundamental Res., Bombay, 1981, pp. 1–39.
(28) Gelbart, S.S.; Knapp, A.W., L-indistinguishability and R groups for thespecial linear group, Adv. in Math. 43 (1982), no. 2, 101–121.
BIBLIOGRAPHY OF STEPHEN S. GELBART xiii
(29) Gelbart, S.; Piatetski-Shapiro, I., Some remarks on metaplectic cusp formsand the correspondences of Shimura and Waldspurger, Israel J. Math. 44(1983), no. 2, 97–126.
(30) Gelbart, Stephen, An elementary introduction to the Langlands program,
Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 177–219.
(31) Gelbart, Stephen; Piatetski-Shapiro, Ilya, Automorphic forms and L-functions for the unitary group, Lie Group Representations, II (College
Park, Md., 1982/1983), Lecture Notes in Math., 1041, Springer, Berlin,
1984, 141–184.
(32) Gelbart, Stephen; Piatetski-Shapiro, Ilya; Rallis, Stephen, Explicit Con-structions of Automorphic L-functions, Lecture Notes in Mathematics
1254 Springer-Verlag, Berlin, 1987.
(33) Gelbart, Stephen; Soudry, David, On Whittaker models and the vanishingof Fourier coefficients of cusp forms, Proc. Indian Acad. Sci. Math. Sci.
97 (1987), no. 1-3, 67–74.
(34) Gelbart, Stephen; Shahidi, Freydoon, Analytic Properties of Automor-phic L-functions, Perspectives in Mathematics 6, Academic Press, Inc.,
Boston, MA, 1988.
(35) Gelbart, S., Recent results on automorphic L-functions, Number Theory,
Trace Formulas and Discrete Groups (Oslo, 1987), Academic Press, Boston,
MA, 1989, pp. 265–280.
(36) Festschrift in Honor of I.I. Piatetski-Shapiro on the Occasion of hisSixtieth Birthday, Part I. Papers in Representation Theory, Papers from
the Workshop on L-Functions, Number Theory, and Harmonic Analysis
held at Tel-Aviv University, Ramat Aviv, May 14–19, 1989 (edited by
S. Gelbart, R. Howe and P. Sarnak), Israel Math. Conf. Proc. 2, Weiz-
mann Science Press of Israel, Jerusalem, 1990.
(37) Gelbart, Stephen S.; Rogawski, Jonathan D., Exceptional representationsand Shimura’s integral for the local unitary group U(3), Festschrift in
Honor of I.I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday,
Part I. (Ramat Aviv, 1989), Israel Math. Conf. Proc. 2, Weizmann
Science Press of Israel, Jerusalem, 1990, pp. 19–75.
(38) Festschrift in Honor of I.I. Piatetski-Shapiro on the Occasion of his Sixti-eth Birthday, Part II. Papers in Analysis, Number Theory and Automor-phic L-functions, Papers from the Workshop on L-Functions, Number
Theory, and Harmonic Analysis held at Tel-Aviv University, Ramat Aviv,
May 14–19, 1989 (edited by S. Gelbart, R. Howe and P. Sarnak), Israel
Math. Conf. Proc. 3, Weizmann Science Press of Israel, Jerusalem, 1990.
(39) Arthur, James; Gelbart, Stephen, Lectures on automorphic L-functions,L-functions and Arithmetic (Durham, 1989), London Math. Soc. Lecture
Note Ser. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 1–59.
(40) Gelbart, Stephen S.; Rogawski, Jonathan D., L-functions and Fourier-Jacobi coefficients for the unitary group U(3), Invent. Math. 105 (1991),
no. 3, 445–472.
(41) Gelbart, Stephen, Automorphic forms and Artin’s conjecture. II, Math-
ematische Wissenschaften gestern und heute, 300 Jahre Mathematische
Gesellschaft in Hamburg, Teil 4 (Hamburg, 1990), Mitt. Math. Ges. Ham-
burg 12 (1991), no. 4, 907–947 (1992).
xiv BIBLIOGRAPHY OF STEPHEN S. GELBART
(42) Gelbart, Stephen, On theta-series liftings for unitary groups, Theta func-
tions: from the classical to the modern, CRM Proc. Lecture Notes 1,
Amer. Math. Soc., Providence, RI, 1993, pp. 129–174.
(43) Gelbart, S.; Rogawski, J.; Soudry, D., On periods of cusp forms and alge-braic cycles for U(3), Israel J. Math. 83 (1993), no. 1-2, 213–252.
(44) Gelbart, Stephen; Rogawski, Jonathan; Soudry, David, Periods of cuspforms and L-packets, C. R. Acad. Sci. Paris Sr. I Math. 317 (1993),
no. 8, 717–722.
(45) The Schur Lectures (1992), Lectures delivered at Tel Aviv University, Tel
Aviv, May 1992 (edited by Ilya Piatetski-Shapiro and Stephen Gelbart),
Israel Math. Conf. Proc. 8, American Mathematical Society, Providence,
RI, 1995.
(46) Gelbart, Stephen, Lectures on the Arthur-Selberg Trace Formula, Univer-
sity Lecture Series 9, American Mathematical Society, Providence, RI,
1996.
(47) Gelbart, Stephen; Rogawski, Jonathan; Soudry, David, Endoscopy, theta-liftings, and period integrals for the unitary group in three variables, Ann.
of Math. (2) 145 (1997), no. 3, 419–476.
(48) Gelbart, Stephen, Three lectures on the modularity of ρE,3 and the Lang-lands reciprocity conjecture, Modular Forms and Fermat’s Last Theorem
(Boston, MA, 1995), Springer, New York, 1997, pp. 155–207.
(49) Friedberg, Solomon; Gelbart, Stephen; Jacquet, Herve; Rogawski,
Jonathan, Representations generiques du groupe unitaire a trois variables(French) [Generic representations for the unitary group in three variables],
C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 4, 255–260.
(50) Piatetski-Shapiro, Ilya, Selected Works of Ilya Piatetski-Shapiro (edited
and with commentaries by James Cogdell, Simon Gindikin, Peter Sar-
nak, Pierre Deligne, Stephen Gelbart, Roger Howe and Stephen Rallis),
American Mathematical Society, Providence, RI, 2000.
(51) Gelbart, Stephen; Shahidi, Freydoon, Boundedness of automorphic L-functions in vertical strips, J. Amer. Math. Soc. 14 (2001), no. 1, 79–107
(electronic).
(52) Gelbart, Stephen; Jacquet, Herve; Rogawski, Jonathan, Generic repre-sentations for the unitary group in three variables, Israel J. Math. 126(2001), 173–237.
(53) Bump, D.; Cogdell, J. W.; de Shalit, E.; Gaitsgory, D.; Kowalski, E.;
Kudla, S. S., An Introduction to the Langlands Program. Lectures Pre-sented at the Hebrew University of Jerusalem, Jerusalem, March 12–16, 2001 (edited by Joseph Bernstein and Stephen Gelbart), Birkhauser
Boston, Inc., Boston, MA, 2003.
(54) Gelbart, Stephen S.; Miller, Stephen D., Riemann’s zeta function andbeyond, Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 1, 59–112 (elec-
tronic).
(55) Gelbart, Stephen, Joe Shalika and the Fine Hall days, 1968–1971, Con-
tributions to Automorphic Forms, Geometry, and Number Theory, ix–xi,
Johns Hopkins Univ. Press, Baltimore, MD, 2004.
BIBLIOGRAPHY OF STEPHEN S. GELBART xv
(56) Gelbart, Stephen S.; Lapid, Erez M.; Sarnak, Peter, A new method forlower bounds of L-functions, C. R. Math. Acad. Sci. Paris 339 (2004),
no. 2, 91–94.
(57) Gelbart, Stephen S.; Lapid, Erez, M. Lower bounds for L-functions at theedge of the critical strip, Amer. J. Math. 128 (2006), no. 3, 619–638.
(58) Gelbart, Stephen, When is an L-function non-vanishing in part of thecritical strip?, Harmonic Analysis, Group Representations, Automorphic
Forms and Invariant Theory, Lect. Notes Ser. Inst. Math. Sci. Natl.
Univ. Singap. 12, World Sci. Publ., Hackensack, NJ, 2007, pp. 73–87.
Conference Program
MONDAY, May 15 (Weizmann Institute)
09:00 - 10:00 Registration of participants
10:00 - 12:30 Morning session on the trace formula
James Arthur (University of Toronto)
14:30 - 15:30 Marie-France Vigneras (Institut Mathematiques de Jussieu)
Irreducibility and cuspidality of the Steinberg representationmodulo p
16:00 - 17:00 Prof. Chaim Leib Pekeris Memorial Lecture by
Peter Sarnak (Princeton University)
Equidistribution and primes
TUESDAY, May 16 (Tel-Aviv University)
10:00 - 12:30 Morning session on L-functions
Daniel Bump (Stanford University)
James Cogdell (Ohio State University)
14:00 - 15:00 Akshay Venkatesh (Courant Institute)
A spherical simple trace formula, and Weyls law for cusp forms
15:30 - 16:30 Wee Teck Gan (University of California, San Diego)
The regularized Siegel-Weil formula for exceptional groups
17:00 - 18:00 Jiu-Kang Yu (Purdue University)
Construction of tame types
WEDNESDAY, May 17 (Weizmann Institute)
10:00 - 12:30 Morning session on theta correspondence
Roger Howe (Yale University)
Stephen Kudla (University of Maryland)
xvii
xviii CONFERENCE PROGRAM
THURSDAY, May 18 (Weizmann Institute)
10:00 - 11:00 Birgit Speh (Cornell University)
The restriction of cohomologically induced representationsto subgroups
11:30 - 12:30 Guy Henniart (University of Paris-Sud)
Explicit local Langlands correspondence for GL(N): the tame case
14:30 - 17:00 Afternoon session on arithmetic applications
Peter Sarnak (Princeton University)
Freydoon Shahidi (Purdue University)
FRIDAY, May 19 (Weizmann Institute)
10:00 - 11:00 Laurent Clozel (University of Paris-Sud)
Equidistribution of adelic tori and of CM-points for Shimuravarieties
11:30 - 12:30 Dinakar Ramakrishnan (Caltech, Pasadena)
Rational cusp forms and Calabi-Yau varieties
14:00 - 15:00 Marko Tadic (University of Zagreb)
On irreducible unitary representations of classical p-adic groups
15:15 - 16:15 Werner Muller (University of Bonn)
The trace formula and the cuspidal spectrum of GL(n)
List of Participants
James Arthur
University of Toronto, Canada
Moshe Baruch
Technion, Israel
Gal Binyamini
Weizmann Institute of Science, Israel
Vladimir Berkovich
Weizmann Institute of Science, Israel
Joseph Bernstein
Tel-Aviv University, Israel
Amnon Besser
Ben Gurion University of the Negev,
Israel
Siegfried Bocherer
University of Mannheim, Germany
Eliot Brenner
Ben Gurion University of the Negev,
Israel
Daniel Bump
Stanford University, U.S.A.
CheeWhye Chin
National University of Singapore,
Singapore
Laurent Clozel
Universite Paris-Sud, France
James Cogdell
Ohio State University, U.S.A.
Ehud de Shalit
Hebrew University of Jerusalem, Israel
Tobias Finis
University of Leipzig, U.S.A.
Solomon Friedberg
Boston College, U.S.A.
Wee Teck Gan
University of California, San Diego,
U.S.A.
Steve Gelbart
Weizmann Institute of Science, Israel
David Ginzburg
Tel-Aviv University, Israel
Nadya Gurevich
Ben Gurion University of the Negev,
Israel
Guy Henniart
Universite Paris-Sud, France
Roger Howe
Yale University, U.S.A.
Joseph Hundley
Pennsylvania State University, U.S.A.
Anthony Joseph
Weizmann Institute of Science, Israel
Martin Karel
Rutgers University, U.S.A.
David Kazhdan
Hebrew University of Jerusalem, Israel
Bernhard Krotz
Max Planck Institute, Bonn, Germany
Stephen Kudla
University of Maryland, U.S.A.
Erez Lapid
Hebrew University of Jerusalem, Israel
xix
xx PARTICIPANTS
Alex Lubotzky
Hebrew University of Jerusalem, Israel
Zhengyu Mao
Rutgers University, U.S.A.
Kimball Martin
Columbia University, U.S.A.
Werner Muller
University of Bonn, Germany
Omer Offen
Weizmann Institute of Science, Israel
Ilya Piatetski-Shapiro
Yale University, U.S.A.
Dipendra Prasad
Tata Institute, India
Dinakar Ramakrishnan
Caltech, Pasadena, U.S.A.
Andre Reznikov
Bar-Ilan University, Israel
Zeev Rudnick
Tel-Aviv University, Israel
Peter Sarnak
Princeton University, U.S.A.
Eitan Sayag
Weizmann Institute of Science, Israel
Freydoon Shahidi
Purdue University, U.S.A.
Lior Silberman
IAS, Princeton, U.S.A.
Andy Sinton
Hebrew University of Jerusalem,Israel
David Soudry
Tel-Aviv University, Israel
Birgit Speh
Cornell University, U.S.A.
Marko Tadic
University of Zagreb, Croatia
Jimi Lee Truelsen
University of Aarhus, Denmark
Yakov Varshavsky
Hebrew University of Jerusalem, Israel
Akshay Venkatesh
Courant Institute, U.S.A.
Marie-France Vigneras
Institut de Mathematiques de Jussieu,
France
David Whitehouse
IHES, Bures-sur-Yvette, France
Jiu-Kang Yu
Purdue University, U.S.A.
Titles in This Subseries
Israel Mathematical Conference Proceedings (IMCP) is a publication, part of the ContemporaryMathematics Series, devoted to the proceedings of conferences, symposia and seminars.Collections of papers focusing on a certain subject will also be published. Prospective volumesmay be submitted to any member of the editorial board. Each volume has an editor (or editors)responsible for its preparation. In order to ensure inexpensive and timely distribution, authorsare requested to submit to the Editor of the volume an electronic TEX file of their manuscript inAMS-LATEX, using the Contemporary Mathematics style file which can be downloaded athttp://www.ams.org/tex/author-info.html. For further information, contact the ManagingEditor, IMCP, Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel;e-mail: rowen@macs.biu.ac.il.
489 David Ginzburg, Erez Lapid, and David Soudry, Editors, Automorphic forms andL-functions II. Local aspects, 2009
488 David Ginzburg, Erez Lapid, and David Soudry, Editors, Automorphic forms andL-functions I. Global aspects, 2009
455 Mark Agranovsky, Daoud Bshouty, Lavi Karp, Simeon Reich, David Shoikhet,and Lawrence Zalcman, Editors, Complex analysis and dynamical systems III, 2008
433 Pavel Etingof, Shlomo Gelaki, and Steven Shnider, Editors, Quantum groups, 2007
404 Alexander Borichev, Hakan Hedenmalm, and Kehe Zhu, Editors, Bergman spacesand related topics in complex analysis, 2006
402 Zvi Arad, Mariagrazia Bianchi, Wolfgang Herfort, Patrizia Longobardi,Mercede Maj, and Carlo Scoppola, Editors, Ischia group theory 2004, 2006
387 Michael Entov, Yehuda Pinchover, and Michah Sageev, Editors, Geometry,spectral theory, groups, and dynamics, 2005
382 Mark Agranovsky, Lavi Karp, and David Shoikhet, Editors, Complex analysis anddynamical systems II, 2005
364 Mark Agranovsky, Lavi Karp, David Shoikhet, and Lawrence Zalcman, Editors,Complex analysis and dynamical systems, 2004
Published Earlier as IMCP
15 Vitali Milman, Iossif Ostrovskii, Mikhail Sodin, Vadim Tkachenko,and Lawrence Zalcman, Editors, Entire functions in modern analysis: Boris Levinmemorial conference, 2001
14 Robert Brooks and Mikhail Sodin, Editors, Lectures in memory of Lars Ahlfors, 2000
13 Yuri Brudnyi, Michael Cwikel, and Yoram Sagher, Editors, Function spaces,
interpolation spaces, and related topics, 1999
12 Mina Teicher, Editor, The heritage of Emmy Noether, 1999
11 Lawrence Zalcman, Editor, Proceedings of the Ashkelon workshop on complex functiontheory (May 1996), 1997
10 Jean-Pierre Fouque, Kenneth J. Hochberg, and Ely Merzbach, Editors,Stochastic analysis: random fields and measure-valued processes, 1995
9 Mina Teicher, Editor, Proceedings of the Hirzebruch 65 conference on algebraicgeometry, 1995
8 Ilya Piatetski-Shapiro and Stephen Gelbart, Editors, The Schur lectures (1992),1995
7 Anthony Joseph and Steven Shnider, Editors, Quantum deformations of algebrasand their representations, 1993
6 Haim Judah, Editor, Set theory of the reals, 1992
5 Michael Cwikel, Mario Milman, and Richard Rochberg, Editors, Interpolationspaces and related topics, 1992
TITLES IN THIS SUBSERIES
4 Simson Baron and Dany Leviatan, Editors, Approximation interpolation andsummability, in honor of Amnon Jakimovski, 1991
3 Stephen Gelbart, Roger Howe, and Peter Sarnak, Editors, Festschrift in honor of I.I. Piatetski-Shapiro, part II: Papers in analysis, number theory and automorphicL-Functions, 1990
2 Stephen Gelbart, Roger Howe, and Peter Sarnak, Editors, Festschrift in honor of I.I. Piatetski-Shapiro, part I: Papers in representation theory, 1990
1 Louis Rowen, Editor, Ring theory, in honor of S. A. Amitsur, 1989
This book is the first of two volumes which represent leading themes of current research in automorphic forms and representation theory of reductive groups over local fields. Articles in this volume mainly represent global aspects of automorphic forms. Among the topics are the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin–Selberg convolutions and �-functions; and ��-adic �-functions. The articles are written by leading researchers in the field, and bring the reader, advanced graduate students and researchers alike, to the frontline of the vigorous research in these deep, vital topics. The companion volume (Contemporary Mathematics, Volume 489) is devoted to local aspects of automorphic forms.
CONM/488www.ams.orgAMS on the Webwww.ams.org