Siegels Modular Forms And Dirichlet Series

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Introduction to Siegel Modular Forms and Dirichlet Series

Author : Anatoli Andrianov
Publisher : Springer Science & Business Media
ISBN 13 : 0387787534
Total Pages : 188 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Introduction to Siegel Modular Forms and Dirichlet Series by : Anatoli Andrianov

Download or read book Introduction to Siegel Modular Forms and Dirichlet Series written by Anatoli Andrianov and published by Springer Science & Business Media. This book was released on 2010-03-17 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several 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.

Siegel's Modular Forms and Dirichlet Series

Author : Hans Maass
Publisher : Springer
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Siegel's Modular Forms and Dirichlet Series by : Hans Maass

Download or read book Siegel's Modular Forms and Dirichlet Series written by Hans Maass and published by Springer. This book was released on 1971 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present the content of a course delivered at the University of Maryland, College Park, between September 1969 and April 1970. The subject is mainly by the intention to show how Atle Selberg makes fascinating use of differential operators in order to prove certain functional equations.

Siegel's Modular Forms and Dirichlet Series

Author : Hans Maaß
Publisher : Springer
ISBN 13 : 3540368817
Total Pages : 334 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Siegel's Modular Forms and Dirichlet Series by : Hans Maaß

Download or read book Siegel's Modular Forms and Dirichlet Series written by Hans Maaß and published by Springer. This book was released on 2006-11-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present the content of a course I delivered at the University of Maryland, College Park, between September 1969 and April 1970. The choice of the subject was mainly determined by my intention to show how Atle Selberg makes fascinating use of differential operators in order to prove certain functional equations. Of course one has to be somewhat familiar with his theory of weakly symmetric Riemannian spaces, but - as Selberg himself pointed out to me the main idea can be found already in Riemann's work. Since Selberg never published his idea, it might be of some value for the mathematical community to make available to a wider public the methods which were originally conceived by Selberg a long time ago.

Introductory Lectures on Siegel Modular Forms

Author : Helmut Klingen
Publisher : Cambridge University Press
ISBN 13 : 0521350522
Total Pages : 0 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Introductory Lectures on Siegel Modular Forms by : Helmut Klingen

Download or read book Introductory Lectures on Siegel Modular Forms written by Helmut Klingen and published by Cambridge University Press. This book was released on 1990-02-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.

The 1-2-3 of Modular Forms

Author : Jan Hendrik Bruinier
Publisher : Springer Science & Business Media
ISBN 13 : 3540741194
Total Pages : 273 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis The 1-2-3 of Modular Forms by : Jan Hendrik Bruinier

Download or read book The 1-2-3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Automorphic Forms and $L$-functions II

Author : David Ginzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821847082
Total Pages : 339 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms and $L$-functions II by : David Ginzburg

Download or read book Automorphic Forms and $L$-functions II written by David Ginzburg and published by American Mathematical Soc.. This book was released on 2009 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821830123
Total Pages : 412 pages
Book Rating : 4.8/5 (31 download)

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Book Synopsis Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth by :

Download or read book Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth written by and published by American Mathematical Soc.. This book was released on 1973 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A two volume collection of mathematical papers on algebra and mathematics in honor of famed Russian mathematician, I.M. Vinogradov.

Automorphic Forms and Zeta Functions

Author : Siegfried Bcherer
Publisher : World Scientific
ISBN 13 : 9812566325
Total Pages : 400 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Automorphic Forms and Zeta Functions by : Siegfried Bcherer

Download or read book Automorphic Forms and Zeta Functions written by Siegfried Bcherer and published by World Scientific. This book was released on 2006 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works. This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operator (H Aoki); Marsden-Weinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S Bocherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K Hashimoto); Skewholomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O(2n)/(O(n) x O(n)) (Y Hironaka & F Sati); Koecher-Maa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L-Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L-Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp(1,q) (Arakawa's Results and Recent Progress) (H Narita); On Modular Forms for the Paramodular Group (B Roberts & R Schmidt); SL(2,Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics.

Modular Forms

Author : Henri Cohen
Publisher : American Mathematical Soc.
ISBN 13 : 0821849476
Total Pages : 714 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Forms by : Henri Cohen

Download or read book Modular Forms written by Henri Cohen and published by American Mathematical Soc.. This book was released on 2017-08-02 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations

Author : Audrey Terras
Publisher : Springer
ISBN 13 : 1493934082
Total Pages : 500 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations by : Audrey Terras

Download or read book Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations written by Audrey Terras and published by Springer. This book was released on 2016-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Automorphic Forms And Zeta Functions - Proceedings Of The Conference In Memory Of Tsuneo Arakawa

Author : Masanobu Kaneko
Publisher : World Scientific
ISBN 13 : 9814478776
Total Pages : 400 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Automorphic Forms And Zeta Functions - Proceedings Of The Conference In Memory Of Tsuneo Arakawa by : Masanobu Kaneko

Download or read book Automorphic Forms And Zeta Functions - Proceedings Of The Conference In Memory Of Tsuneo Arakawa written by Masanobu Kaneko and published by World Scientific. This book was released on 2006-01-03 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works.This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions.

Modular Forms, a Computational Approach

Author : William A. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 0821839608
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Forms, a Computational Approach by : William A. Stein

Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro

Author : James W. Cogdell
Publisher : American Mathematical Soc.
ISBN 13 : 0821893947
Total Pages : 454 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro by : James W. Cogdell

Download or read book Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro written by James W. Cogdell and published by American Mathematical Soc.. This book was released on 2014-04-01 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytic Number Theory, Modular Forms and q-Hypergeometric Series

Author : George E. Andrews
Publisher : Springer
ISBN 13 : 3319683764
Total Pages : 764 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Analytic Number Theory, Modular Forms and q-Hypergeometric Series by : George E. Andrews

Download or read book Analytic Number Theory, Modular Forms and q-Hypergeometric Series written by George E. Andrews and published by Springer. This book was released on 2018-02-01 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.

Automorphic Forms and Geometry of Arithmetic Varieties

Author : K. Hashimoto
Publisher : Academic Press
ISBN 13 : 1483218074
Total Pages : 540 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Automorphic Forms and Geometry of Arithmetic Varieties by : K. Hashimoto

Download or read book Automorphic Forms and Geometry of Arithmetic Varieties written by K. Hashimoto and published by Academic Press. This book was released on 2014-07-14 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.

Encyclopedic Dictionary of Mathematics

Author : Nihon Sūgakkai
Publisher : MIT Press
ISBN 13 : 9780262590204
Total Pages : 1180 pages
Book Rating : 4.5/5 (92 download)

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Book Synopsis Encyclopedic Dictionary of Mathematics by : Nihon Sūgakkai

Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.

Siegel Modular Forms

Author : Ameya Pitale
Publisher : Springer
ISBN 13 : 3030156753
Total Pages : 142 pages
Book Rating : 4.0/5 (31 download)

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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 142 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.