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 Lectures on Siegel Modular Forms and Representation by Quadratic Forms written by Yoshiyuki Kitaoka and published by . This book was released on 1986 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 Lectures on Modular Forms written by Robert C. Gunning and published by Princeton University Press. This book was released on 1962-03-21 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone.
Download or read book Introduction to Siegel Modular Forms and Dirichlet Series written by Anatoli Andrianov and published by Springer. This book was released on 2010-11-15 with total page 184 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 Modular Forms written by Joseph J. Lehner and published by Courier Dover Publications. This book was released on 2017-05-17 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise book offers expository account of theory of modular forms and its application to number theory and analysis. Substantial notes at the end of each chapter amplify the more difficult subjects. 1969 edition.
Download or read book Lectures on Modular Forms written by Joseph Lehner and published by . This book was released on 1969 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modular Forms A Classical And Computational Introduction 2nd Edition written by Lloyd James Peter 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.
Download or read book Modular Forms and Galois Cohomology written by Haruzo Hida and published by Cambridge University Press. This book was released on 2000-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.
Download or read book Lectures on Siegel s Modular Functions written by Hans Maass and published by . This book was released on 1954 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Siegel s Modular Forms and Dirichlet Series written by Hans Maass and published by . This book was released on 2014-09-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Modular Forms written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#
Download or read book Siegel s modular forms and Dirichlet series written by Hans Maaß and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Modular Forms and Related Topics in Number Theory written by B. Ramakrishnan and published by Springer Nature. This book was released on 2020-11-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.
