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

Rainer Weissauer
Endoscopy for GSp 4 and the Cohomology of Siegel Modular Threefolds Book PDF

Author : Rainer Weissauer
Publisher : Springer
Page : 384 pages
File Size : 48,8 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783540893066

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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds by Rainer Weissauer Pdf

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

Rainer Weissauer
Endoscopy for GSp 4 and the Cohomology of Siegel Modular Threefolds Book PDF

Author : Rainer Weissauer
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 52,5 Mb
Release : 2009-03-25
Category : Mathematics
ISBN : 9783540893059

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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds by Rainer Weissauer Pdf

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.

L-Functions and Automorphic Forms

Jan Hendrik Bruinier,Winfried Kohnen
L Functions and Automorphic Forms Book PDF

Author : Jan Hendrik Bruinier,Winfried Kohnen
Publisher : Springer
Page : 366 pages
File Size : 55,5 Mb
Release : 2018-02-22
Category : Mathematics
ISBN : 9783319697123

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L-Functions and Automorphic Forms by Jan Hendrik Bruinier,Winfried Kohnen Pdf

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.

Siegel Modular Forms

Ameya Pitale
Siegel Modular Forms Book PDF

Author : Ameya Pitale
Publisher : Springer
Page : 138 pages
File Size : 43,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030156756

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Siegel Modular Forms by Ameya Pitale Pdf

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.

Transfer of Siegel Cusp Forms of Degree 2

Ameya Pitale,Abhishek Saha,Ralf Schmidt
Transfer of Siegel Cusp Forms of Degree 2 Book PDF

Author : Ameya Pitale,Abhishek Saha,Ralf Schmidt
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 55,9 Mb
Release : 2014-09-29
Category : Mathematics
ISBN : 9780821898567

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Transfer of Siegel Cusp Forms of Degree 2 by Ameya Pitale,Abhishek Saha,Ralf Schmidt Pdf

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

Intersection Spaces, Spatial Homology Truncation, and String Theory

Markus Banagl
Intersection Spaces Spatial Homology Truncation and String Theory Book PDF

Author : Markus Banagl
Publisher : Springer
Page : 224 pages
File Size : 45,7 Mb
Release : 2010-06-16
Category : Mathematics
ISBN : 9783642125898

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Intersection Spaces, Spatial Homology Truncation, and String Theory by Markus Banagl Pdf

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This 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. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

Lévy Matters I

Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
L vy Matters I Book PDF

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 42,5 Mb
Release : 2010-09-05
Category : Mathematics
ISBN : 9783642140068

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

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

Hans Schoutens
The Use of Ultraproducts in Commutative Algebra Book PDF

Author : Hans Schoutens
Publisher : Springer
Page : 210 pages
File Size : 47,8 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9783642133688

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The Use of Ultraproducts in Commutative Algebra by Hans Schoutens Pdf

In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.

Regularity and Approximability of Electronic Wave Functions

Harry Yserentant
Regularity and Approximability of Electronic Wave Functions Book PDF

Author : Harry Yserentant
Publisher : Springer
Page : 188 pages
File Size : 49,6 Mb
Release : 2010-05-19
Category : Mathematics
ISBN : 9783642122484

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Regularity and Approximability of Electronic Wave Functions by Harry Yserentant Pdf

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.

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Christian Pötzsche
Geometric Theory of Discrete Nonautonomous Dynamical Systems Book PDF

Author : Christian Pötzsche
Publisher : Springer
Page : 399 pages
File Size : 41,5 Mb
Release : 2010-08-24
Category : Mathematics
ISBN : 9783642142581

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Geometric Theory of Discrete Nonautonomous Dynamical Systems by Christian Pötzsche Pdf

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

Polyharmonic Boundary Value Problems

Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers
Polyharmonic Boundary Value Problems Book PDF

Author : Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers
Publisher : Springer
Page : 423 pages
File Size : 51,8 Mb
Release : 2010-05-26
Category : Mathematics
ISBN : 9783642122453

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Polyharmonic Boundary Value Problems by Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers Pdf

This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Holomorphic Dynamical Systems

Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Holomorphic Dynamical Systems Book PDF

Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 53,6 Mb
Release : 2010-07-31
Category : Mathematics
ISBN : 9783642131707

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Holomorphic Dynamical Systems by Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate Pdf

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

Topics in Algebraic and Topological K-Theory

Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Topics in Algebraic and Topological K Theory Book PDF

Author : Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer
Page : 308 pages
File Size : 50,6 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642157080

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

The Analysis of Fractional Differential Equations

Kai Diethelm
The Analysis of Fractional Differential Equations Book PDF

Author : Kai Diethelm
Publisher : Springer
Page : 247 pages
File Size : 46,5 Mb
Release : 2010-08-18
Category : Mathematics
ISBN : 9783642145742

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The Analysis of Fractional Differential Equations by Kai Diethelm Pdf

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.