Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds
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Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds
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Author : Rainer Weissauer
language : en
Publisher: Springer
Release Date : 2009-04-28
Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds written by Rainer Weissauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Mathematics categories.
This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in [115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan’s conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.
Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds
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Author : Rainer Weissauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-25
Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds written by Rainer Weissauer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-25 with Mathematics categories.
The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic of higher dimensional modular varieties. For Siegel modular threefolds some basic results on their cohomology groups are derived in this book from considering topological trace formulas.
Parahoric Restriction For Gsp 4 And The Inner Cohomology Of Siegel Modular Threefolds
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Author : Mirko Rösner
language : en
Publisher:
Release Date : 2016
Parahoric Restriction For Gsp 4 And The Inner Cohomology Of Siegel Modular Threefolds written by Mirko Rösner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
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 area as 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.
L Functions And Automorphic Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2018-02-22
L Functions And Automorphic Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.
This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.
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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Intersection Spaces Spatial Homology Truncation And String Theory
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Author : Markus Banagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-08
Intersection Spaces Spatial Homology Truncation And String Theory written by Markus Banagl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-08 with Mathematics categories.
The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality.
L Vy Matters I
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Author : Thomas Duquesne
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-05
L Vy Matters I written by Thomas Duquesne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-05 with Mathematics categories.
Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
The Use Of Ultraproducts In Commutative Algebra
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Author : Hans Schoutens
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-31
The Use Of Ultraproducts In Commutative Algebra written by Hans Schoutens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-31 with Mathematics categories.
Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
Regularity And Approximability Of Electronic Wave Functions
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Author : Harry Yserentant
language : en
Publisher: Springer
Release Date : 2010-05-19
Regularity And Approximability Of Electronic Wave Functions written by Harry Yserentant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-19 with Mathematics categories.
The electronic Schrodi ̈ nger equation describes the motion of N electrons under Coulomb interaction forces in a eld of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial dimensions for each electron. Approxim- ing the solutions is thus inordinately challenging, and it is conventionally believed that a reduction to simpli ed models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to c- vince the reader that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The present notes arose from lectures that I gave in Berlin during the academic year 2008/09 to introduce beginning graduate students of mathematics into this subject. They are kept on an intermediate level that should be accessible to an audience of this kind as well as to physicists and theoretical chemists with a c- responding mathematical training.