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 2008-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to present a straightforward and easily accessible survey of the analytic theory of quadratic forms. Written at an elementary level, the book provides a sound basis from which the reader can study advanced works and undertake original research. Roughly half a century ago C.L. Siegel discovered a new type of automorphic forms in several variables in connection with his famous work on the analytic theory of quadratic forms. Since then 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 recent arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The text is based on the author's lectures given over a number of years and is intended for a one semester graduate course, although it can serve equally well for self study . The only prerequisites are a knowledge of algebra, number theory and complex analysis.
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.
Download or read book Lectures on Siegel Modular Forms and Representation by Quadratic Forms written by Yoshiyuki Kitaoka and published by Springer. This book was released on 1986-09-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published for the Tata Institute of Fundamental Research
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.
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.
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.
Download or read book Transfer of Siegel Cusp Forms of Degree 2 written by Ameya Pitale and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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.
Download or read book Automorphic Forms written by Bernhard Heim and published by Springer. This book was released on 2014-11-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.
Download or read book Stable Klingen Vectors and Paramodular Newforms written by Jennifer Johnson-Leung and published by Springer Nature. This book was released on 2023-12-27 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level. It introduces the family of stable Klingen congruence subgroups of GSp(4) and uses this family to obtain new relations between the Hecke eigenvalues and Fourier coefficients of paramodular newforms, revealing a fundamental dichotomy for paramodular representations. Among other important results, it includes a complete description of the vectors fixed by these congruence subgroups in all irreducible representations of GSp(4) over a nonarchimedean local field. Siegel paramodular forms have connections with the theory of automorphic representations and the Langlands program, Galois representations, the arithmetic of abelian surfaces, and algorithmic number theory. Providing a useful standard source on the subject, the book will be of interest to graduate students and researchers working in the above fields.
Download or read book Automorphic Forms Automorphic Representations and Arithmetic written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 1999 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Geometry and Analysis of Automorphic Forms of Several Variables written by Yoshinori Hamahata and published by World Scientific. This book was released on 2012 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers OCA Java exam 1Z0-850.This is an entry level Java cert exam. All you need is to pass one exam 1Z0-850 in order to pass. The topics covered include:Fundamental Object-Oriented ConceptsJava Implementation of Object-Oriented ConceptsAlgorithm Design and ImplementationJava Development FundamentalsJava Platforms and Integration TechnologiesClient TechnologiesServer TechnologiesWe give you knowledge information relevant to the exam specifications. To be able to succeed in the real exam, you'll need to apply your earned knowledge to the question scenarios. This ExamFOCUS book focuses on the more difficult topics that will likely make a difference in exam results.
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.
Download or read book Number Theory and Applications written by S.D. Adhikari and published by Springer. This book was released on 2009-06-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.
Download or read book Multiple Dirichlet Series L functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.
Download or read book Modular Forms written by L J P Kilford and published by World Scientific Publishing Company. This book was released on 2015-03-12 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it. This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.
