Electronic ISBN:  9781470430054 
Product Code:  CONM/664.E 
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Book DetailsContemporary MathematicsVolume: 664; 2016; 376 ppMSC: Primary 11; 22;
This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their \(L\)functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna.
The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their \(L\)functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of \(p\)adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, \(L\)functions for classical groups, special values of \(L\)functions, Howe duality, subconvexity for \(L\)functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on \(L\)functions, nodal sets and geometry.ReadershipGraduate students and research mathematicians interested in automorphic forms and number theory.

Table of Contents

Articles

Mahdi Asgari, James W. Cogdell and Freydoon Shahidi  Local transfer and reducibility of induced representations of $p$adic groups of classical type

A. I. Badulescu and G. Henniart  Shintani relation for base change: unitary and elliptic representations

Asher BenArtzi and David Soudry  On $L$functions for $\textup {U}_{2k}\times \textup {R}_{E/F}\textup {GL}_m$, ($k<m$)

Wee Teck Gan and Shuichiro Takeda  On the Howe duality conjecture in classical theta correspondence

Harald Grobner, Michael Harris and Erez Lapid  Whittaker rational structures and special values of the Asai $L$function

Roman Holowinsky, Ritabrata Munshi and Zhi Qi  Character sums of composite moduli and hybrid subconvexity

Roger Howe  A linear algebra description of $K_{\mathbb C}\setminus G_{\mathbb C} / B_{\mathbb C}$ for classical groups

Hervé Jacquet  Germs for Kloosterman integrals, a review

Dihua Jiang and Baiying Liu  Fourier coefficients for automorphic forms on quasisplit classical groups

JuLee Kim  A generalized Casselman–Shalika formula on $GL_{N}$

Henry H. Kim and Takuya Yamauchi  A conditional construction of Artin representations for real analytic Siegel cusp forms of weight $(2,1)$

Stephen Kudla  Another product for a Borcherds form

Erez Lapid and Zhengyu Mao  On Whittaker–Fourier coefficients of automorphic forms on unitary groups: reduction to a local identity

J. Nekovář and A. J. Scholl  Introduction to plectic cohomology

Kimball Martin and Dinakar Ramakrishnan  A comparison of automorphic and Artin Lseries of GL(2)type agreeing at degree one primes

Peter Sarnak and Igor Wigman  Topologies of nodal sets of random band limited functions

Joachim Schwermer and Christoph Waldner  Geometric cycles, classical groups and related cohomology classes for arithmetic groups


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This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their \(L\)functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna.
The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their \(L\)functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of \(p\)adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, \(L\)functions for classical groups, special values of \(L\)functions, Howe duality, subconvexity for \(L\)functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on \(L\)functions, nodal sets and geometry.
Graduate students and research mathematicians interested in automorphic forms and number theory.

Articles

Mahdi Asgari, James W. Cogdell and Freydoon Shahidi  Local transfer and reducibility of induced representations of $p$adic groups of classical type

A. I. Badulescu and G. Henniart  Shintani relation for base change: unitary and elliptic representations

Asher BenArtzi and David Soudry  On $L$functions for $\textup {U}_{2k}\times \textup {R}_{E/F}\textup {GL}_m$, ($k<m$)

Wee Teck Gan and Shuichiro Takeda  On the Howe duality conjecture in classical theta correspondence

Harald Grobner, Michael Harris and Erez Lapid  Whittaker rational structures and special values of the Asai $L$function

Roman Holowinsky, Ritabrata Munshi and Zhi Qi  Character sums of composite moduli and hybrid subconvexity

Roger Howe  A linear algebra description of $K_{\mathbb C}\setminus G_{\mathbb C} / B_{\mathbb C}$ for classical groups

Hervé Jacquet  Germs for Kloosterman integrals, a review

Dihua Jiang and Baiying Liu  Fourier coefficients for automorphic forms on quasisplit classical groups

JuLee Kim  A generalized Casselman–Shalika formula on $GL_{N}$

Henry H. Kim and Takuya Yamauchi  A conditional construction of Artin representations for real analytic Siegel cusp forms of weight $(2,1)$

Stephen Kudla  Another product for a Borcherds form

Erez Lapid and Zhengyu Mao  On Whittaker–Fourier coefficients of automorphic forms on unitary groups: reduction to a local identity

J. Nekovář and A. J. Scholl  Introduction to plectic cohomology

Kimball Martin and Dinakar Ramakrishnan  A comparison of automorphic and Artin Lseries of GL(2)type agreeing at degree one primes

Peter Sarnak and Igor Wigman  Topologies of nodal sets of random band limited functions

Joachim Schwermer and Christoph Waldner  Geometric cycles, classical groups and related cohomology classes for arithmetic groups