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Endoscopy For Gsp4 And The Cohomology Of Siegel Modular Threefolds
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Book Synopsis Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds by : Rainer Weissauer
Download or read book Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds written by Rainer Weissauer and published by Springer. This book was released on 2009-04-28 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds by : Rainer Weissauer
Download or read book Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds written by Rainer Weissauer and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis L-Functions and Automorphic Forms by : Jan Hendrik Bruinier
Download or read book L-Functions and Automorphic Forms written by Jan Hendrik Bruinier and published by Springer. This book was released on 2018-02-22 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Siegel Modular Forms by : Ameya Pitale
Download or read book Siegel Modular Forms written by Ameya Pitale and published by Springer. This book was released on 2019-05-07 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms by : Kazuyuki Hatada
Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Intersection Spaces, Spatial Homology Truncation, and String Theory by : Markus Banagl
Download or read book Intersection Spaces, Spatial Homology Truncation, and String Theory written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Use of Ultraproducts in Commutative Algebra by : Hans Schoutens
Download or read book The Use of Ultraproducts in Commutative Algebra written by Hans Schoutens and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Regularity and Approximability of Electronic Wave Functions by : Harry Yserentant
Download or read book Regularity and Approximability of Electronic Wave Functions written by Harry Yserentant and published by Springer. This book was released on 2010-05-19 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Holomorphic Dynamical Systems by : Nessim Sibony
Download or read book Holomorphic Dynamical Systems written by Nessim Sibony and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche
Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer. This book was released on 2010-08-24 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Polyharmonic Boundary Value Problems by : Filippo Gazzola
Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics in Algebraic and Topological K-Theory by : Paul Frank Baum
Download or read book Topics in Algebraic and Topological K-Theory written by Paul Frank Baum and published by Springer. This book was released on 2010-10-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Morrey and Campanato Meet Besov, Lizorkin and Triebel by : Wen Yuan
Download or read book Morrey and Campanato Meet Besov, Lizorkin and Triebel written by Wen Yuan and published by Springer. This book was released on 2010-09-02 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer Science & Business Media. This book was released on 2010-09-03 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Catherine Donati Martin Publisher :Springer Science & Business Media ISBN 13 :3642152163 Total Pages :511 pages Book Rating :4.6/5 (421 download)
Book Synopsis Séminaire de Probabilités XLIII by : Catherine Donati Martin
Download or read book Séminaire de Probabilités XLIII written by Catherine Donati Martin and published by Springer Science & Business Media. This book was released on 2010-10-28 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.
Book Synopsis Arithmetic Geometry by : Jean-Louis Colliot-Thélène
Download or read book Arithmetic Geometry written by Jean-Louis Colliot-Thélène and published by Springer. This book was released on 2010-10-27 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.
