eBook ISBN:  9780821876381 
Product Code:  CONM/53.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876381 
Product Code:  CONM/53.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 53; 1986; 554 ppMSC: Primary 11
This volume provides both a good introduction to current work and a collection of survey articles on the Selberg trace formula and its applications. As the proceedings of a joint AMSIMSSIAM Summer Research Conference, this material represents a diverse set of attitudes toward the trace formula, including those from mathematical physics, classical analytic and modern adelic number theory, modern geometric representations, and classical harmonic analysis.
The background required varies considerably, from introductory papers to those requiring familiarity with representation theory, the theory of automorphic forms, and number theory.

Table of Contents

Articles

Jeffrey Adams and Joseph F. Johnson — Endoscopic groups and stable packets of certain derived functor modules [ MR 853549 ]

Dorothy Wallace Andreoli — A preliminary version of the Selberg trace formula for ${\rm PSL}(3,{\bf Z})\backslash {\rm PSL}(3,{\bf R})/{\rm SO}(3,{\bf R})$ [ MR 853550 ]

James Arthur, Rebecca A. Herb and Paul J. Sally, Jr. — The Fourier transform of weighted orbital integrals on ${\rm SL}(2,{\bf R})$ [ MR 853551 ]

Daniel Bump, Solomon Friedberg and Dorian Goldfeld — Poincaré series and Kloosterman sums [ MR 853552 ]

J.M. Deshouillers and H. Iwaniec — The nonvanishing of RankinSelberg zetafunctions at special points [ MR 853553 ]

Jürgen Elstrodt, Fritz Grunewald and Jens Mennicke — Eisenstein series for imaginary quadratic number fields [ MR 853554 ]

Yuval Z. Flicker — Unitary quasilifting: preparations [ MR 853555 ]

David Fried — Fuchsian groups and Reidemeister torsion [ MR 853556 ]

Paul B. Garrett — Thetacorrespondences on unitary groups [ MR 853557 ]

Paul Gérardin and WenCh’ing Winnie Li — Establishing correspondences without the trace formula [ MR 853558 ]

George T. Gilbert — Multiplicity theorems for ${\rm GL}(2)$ and ${\rm GL}(3)$ [ MR 853559 ]

A. Good — The convolution method for Dirichlet series [ MR 853560 ]

Martin C. Gutzwiller — Physics and Selberg’s trace formula [ MR 853561 ]

Kiichiro Hashimoto — Representations of the finite symplectic group ${\rm Sp}(4,{\bf F}_p)$ in the spaces of Siegel modular forms [ MR 853562 ]

Dennis A. Hejhal — Roots of quadratic congruences and eigenvalues of the nonEuclidean Laplacian [ MR 853563 ]

M. N. Huxley — Exceptional eigenvalues and congruence subgroups [ MR 853564 ]

Hervé Jacquet — An introduction to the trace formula from the adelic point of view [ MR 853565 ]

N. Mandouvalos — The theory of Eisenstein series for Kleinian groups [ MR 853566 ]

M. Scott Osborne — The continuous spectrum: some explicit formulas [ MR 853567 ]

M. Scott Osborne — Selberg’s trace formula and a character identity for generalized Heisenberg groups [ MR 853568 ]

J. D. Rogawski — Some remarks on Shalika germs [ MR 853569 ]

Peter Sarnak — On cusp forms [ MR 853570 ]

Audrey A. Terras — Some simple aspects of the theory of automorphic forms for ${\rm GL}(n,{\bf Z})$ [ MR 853571 ]

V. S. Varadarajan — The eigenvalue problem on negatively curved compact locally symmetric manifolds [ MR 853572 ]

MarieFrance Vignéras — Correspondances entre representations automorphes de ${\rm GL}(2)$ sur une extension quadratique de ${\rm GSp}(4)$ sur ${\bf Q}$, conjecture locale de Langlands pour ${\rm GSp}(4)$ [ MR 853573 ]

Garth Warner — Traceability on the discrete spectrum [ MR 853574 ]

Rainer Weissauer — Stable modular forms [ MR 853575 ]

Floyd L. Williams — Finite spaces of nonclassical Poincaré theta series [ MR 853576 ]


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This volume provides both a good introduction to current work and a collection of survey articles on the Selberg trace formula and its applications. As the proceedings of a joint AMSIMSSIAM Summer Research Conference, this material represents a diverse set of attitudes toward the trace formula, including those from mathematical physics, classical analytic and modern adelic number theory, modern geometric representations, and classical harmonic analysis.
The background required varies considerably, from introductory papers to those requiring familiarity with representation theory, the theory of automorphic forms, and number theory.

Articles

Jeffrey Adams and Joseph F. Johnson — Endoscopic groups and stable packets of certain derived functor modules [ MR 853549 ]

Dorothy Wallace Andreoli — A preliminary version of the Selberg trace formula for ${\rm PSL}(3,{\bf Z})\backslash {\rm PSL}(3,{\bf R})/{\rm SO}(3,{\bf R})$ [ MR 853550 ]

James Arthur, Rebecca A. Herb and Paul J. Sally, Jr. — The Fourier transform of weighted orbital integrals on ${\rm SL}(2,{\bf R})$ [ MR 853551 ]

Daniel Bump, Solomon Friedberg and Dorian Goldfeld — Poincaré series and Kloosterman sums [ MR 853552 ]

J.M. Deshouillers and H. Iwaniec — The nonvanishing of RankinSelberg zetafunctions at special points [ MR 853553 ]

Jürgen Elstrodt, Fritz Grunewald and Jens Mennicke — Eisenstein series for imaginary quadratic number fields [ MR 853554 ]

Yuval Z. Flicker — Unitary quasilifting: preparations [ MR 853555 ]

David Fried — Fuchsian groups and Reidemeister torsion [ MR 853556 ]

Paul B. Garrett — Thetacorrespondences on unitary groups [ MR 853557 ]

Paul Gérardin and WenCh’ing Winnie Li — Establishing correspondences without the trace formula [ MR 853558 ]

George T. Gilbert — Multiplicity theorems for ${\rm GL}(2)$ and ${\rm GL}(3)$ [ MR 853559 ]

A. Good — The convolution method for Dirichlet series [ MR 853560 ]

Martin C. Gutzwiller — Physics and Selberg’s trace formula [ MR 853561 ]

Kiichiro Hashimoto — Representations of the finite symplectic group ${\rm Sp}(4,{\bf F}_p)$ in the spaces of Siegel modular forms [ MR 853562 ]

Dennis A. Hejhal — Roots of quadratic congruences and eigenvalues of the nonEuclidean Laplacian [ MR 853563 ]

M. N. Huxley — Exceptional eigenvalues and congruence subgroups [ MR 853564 ]

Hervé Jacquet — An introduction to the trace formula from the adelic point of view [ MR 853565 ]

N. Mandouvalos — The theory of Eisenstein series for Kleinian groups [ MR 853566 ]

M. Scott Osborne — The continuous spectrum: some explicit formulas [ MR 853567 ]

M. Scott Osborne — Selberg’s trace formula and a character identity for generalized Heisenberg groups [ MR 853568 ]

J. D. Rogawski — Some remarks on Shalika germs [ MR 853569 ]

Peter Sarnak — On cusp forms [ MR 853570 ]

Audrey A. Terras — Some simple aspects of the theory of automorphic forms for ${\rm GL}(n,{\bf Z})$ [ MR 853571 ]

V. S. Varadarajan — The eigenvalue problem on negatively curved compact locally symmetric manifolds [ MR 853572 ]

MarieFrance Vignéras — Correspondances entre representations automorphes de ${\rm GL}(2)$ sur une extension quadratique de ${\rm GSp}(4)$ sur ${\bf Q}$, conjecture locale de Langlands pour ${\rm GSp}(4)$ [ MR 853573 ]

Garth Warner — Traceability on the discrete spectrum [ MR 853574 ]

Rainer Weissauer — Stable modular forms [ MR 853575 ]

Floyd L. Williams — Finite spaces of nonclassical Poincaré theta series [ MR 853576 ]