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The Selberg Trace Formula and Related Topics
 
Edited by: Dennis A. Hejhal
Peter Sarnak
Anne Audrey
The Selberg Trace Formula and Related Topics
eBook ISBN:  978-0-8218-7638-1
Product Code:  CONM/53.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
The Selberg Trace Formula and Related Topics
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The Selberg Trace Formula and Related Topics
Edited by: Dennis A. Hejhal
Peter Sarnak
Anne Audrey
eBook ISBN:  978-0-8218-7638-1
Product Code:  CONM/53.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 53; 1986; 554 pp
    MSC: 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 AMS-IMS-SIAM 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 Rankin-Selberg zeta-functions 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 — Theta-correspondences on unitary groups [ MR 853557 ]
    • Paul Gérardin and Wen-Ch’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 ]
    • Ki-ichiro 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 non-Euclidean 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 ]
    • Marie-France 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 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 53; 1986; 554 pp
MSC: 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 AMS-IMS-SIAM 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 Rankin-Selberg zeta-functions 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 — Theta-correspondences on unitary groups [ MR 853557 ]
  • Paul Gérardin and Wen-Ch’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 ]
  • Ki-ichiro 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 non-Euclidean 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 ]
  • Marie-France 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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Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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