Transfer Of Siegel Cusp Forms Of Degree 2
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Transfer Of Siegel Cusp Forms Of Degree 2
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Author : Ameya Pitale
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29
Transfer Of Siegel Cusp Forms Of Degree 2 written by Ameya Pitale and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and
Transfer Of Siegel Cusp Forms Of Degree 2
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Author : Ameya Pitale
language : en
Publisher:
Release Date : 2014
Transfer Of Siegel Cusp Forms Of Degree 2 written by Ameya Pitale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Cusp forms (Mathematics) categories.
Let π π be the automorphic representation of GSp4(A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and τ be an arbitrary cuspidal, automorphic representation of GL2(A). Using Furusawa's integral representation for GSp4 × GL2 combined with a pullback formula involving the unitary group GU(3,3), we prove that the L-functions L(s,π×τ) are “nice”. The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations π π have a functorial lifting to a cuspidal representation of GL4(A). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of π to a cuspidal representation of GL5(A). As an application, we obtain analytic properties of various L L-functions related to full level Siegel cusp forms. We also obtain special value results for GSp4 × GL1 and GSp4 × GL2.
Siegel Modular Forms
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Author : Ameya Pitale
language : en
Publisher: Springer
Release Date : 2019-05-07
Siegel Modular Forms written by Ameya Pitale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the areaas a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro
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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-01
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro written by James W. Cogdell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-01 with Mathematics categories.
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms
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Author : Kazuyuki Hatada
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms written by Kazuyuki Hatada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.
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Period Functions For Maass Wave Forms And Cohomology
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Author : R. Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Period Functions For Maass Wave Forms And Cohomology written by R. Bruggeman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.
Poincare Einstein Holography For Forms Via Conformal Geometry In The Bulk
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Author : A. Rod Gover
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Poincare Einstein Holography For Forms Via Conformal Geometry In The Bulk written by A. Rod Gover and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.
Complex Analysis Of Several Variables
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Author : Yum-Tong Siu
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Complex Analysis Of Several Variables written by Yum-Tong Siu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Presents a collection of papers from the Symposium on Several Complex Variables held April 12-15, 1983 in Madison, Wisconsin. This book contains a selection of the presented papers as well as some contributed papers.
On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp 4 The Fundamental Lemma
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Author : Masaaki Furusawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp 4 The Fundamental Lemma written by Masaaki Furusawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
On Central Critical Values Of The Degree Four L Functions For Gsp 4 The Fundamental Lemma Iii
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Author : Masaaki Furusawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
On Central Critical Values Of The Degree Four L Functions For Gsp 4 The Fundamental Lemma Iii written by Masaaki Furusawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Mathematics categories.
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.