Fourier Coefficients of Automorphic Forms
Author: R. W. Bruggeman
Publisher: Springer
Published: 2006-11-15
Total Pages: 205
ISBN-13: 3540387269
DOWNLOAD EBOOKPosts
Representations of SU(2,1) in Fourier Term Modules
Author: Roelof W. Bruggeman
Publisher: Springer Nature
Published: 2023-11-06
Total Pages: 217
ISBN-13: 3031431928
DOWNLOAD EBOOKThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
Modular forms and Hecke operators
Author: A. N. Andrianov V. G. Zhuravlev
Publisher: American Mathematical Soc.
Published: 1995-08-28
Total Pages: 350
ISBN-13: 9780821897621
DOWNLOAD EBOOKThe concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Relative Trace Formulas
Author: Werner Müller
Publisher: Springer Nature
Published: 2021-05-18
Total Pages: 438
ISBN-13: 3030685063
DOWNLOAD EBOOKA series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.
Introduction to Siegel Modular Forms and Dirichlet Series
Author: Anatoli Andrianov
Publisher: Springer Science & Business Media
Published: 2010-03-17
Total Pages: 188
ISBN-13: 0387787534
DOWNLOAD EBOOKSeveral years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.
The 1-2-3 of Modular Forms
Author: Jan Hendrik Bruinier
Publisher: Springer Science & Business Media
Published: 2008-02-10
Total Pages: 273
ISBN-13: 3540741194
DOWNLOAD EBOOKThis book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Mathematical Methods for Physicists
Author: George Brown Arfken
Publisher: Academic Press
Published: 2013
Total Pages: 1230
ISBN-13: 0123846544
DOWNLOAD EBOOKTable of Contents Mathematical Preliminaries Determinants and Matrices Vector Analysis Tensors and Differential Forms Vector Spaces Eigenvalue Problems Ordinary Differential Equations Partial Differential Equations Green's Functions Complex Variable Theory Further Topics in Analysis Gamma Function Bessel Functions Legendre Functions Angular Momentum Group Theory More Special Functions Fourier Series Integral Transforms Periodic Systems Integral Equations Mathieu Functions Calculus of Variations Probability and Statistics.
Automorphic Forms
Author: Anton Deitmar
Publisher: Springer Science & Business Media
Published: 2012-08-29
Total Pages: 255
ISBN-13: 144714435X
DOWNLOAD EBOOKAutomorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Automorphic Forms, Representations and $L$-Functions
Author: A. Borel
Publisher: American Mathematical Soc.
Published: 1979
Total Pages: 334
ISBN-13: 0821814354
DOWNLOAD EBOOKContains sections on Reductive groups, representations, Automorphic forms and representations.
From Classical Analysis to Analysis on Fractals
Author: Patricia Alonso Ruiz
Publisher: Springer Nature
Published: 2023-11-25
Total Pages: 294
ISBN-13: 3031378008
DOWNLOAD EBOOKOver the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
