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Introductory Lectures on Siegel Modular Forms

2008-05-15 Mathematics
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Release : 2008-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 091/5 ( reviews)

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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. This book was released on 2008-05-15. 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.

Lectures on Siegel Modular Forms and Representation by Quadratic Forms

1986 Forms (Mathematics).
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Release : 1986
Genre : Forms (Mathematics).
Kind : eBook
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Book Synopsis Lectures on Siegel Modular Forms and Representation by Quadratic Forms by : Yoshiyuki Kitaoka

Download or read book Lectures on Siegel Modular Forms and Representation by Quadratic Forms written by Yoshiyuki Kitaoka. This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Siegel Modular Forms and Dirichlet Series

2010-03-17 Mathematics
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Release : 2010-03-17
Genre : Mathematics
Kind : eBook
Book Rating : 534/5 ( reviews)

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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. This book was released on 2010-03-17. 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 Modular Forms

2019-05-07 Mathematics
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Release : 2019-05-07
Genre : Mathematics
Kind : eBook
Book Rating : 753/5 ( reviews)

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Book Synopsis Siegel Modular Forms by : Ameya Pitale

Download or read book Siegel Modular Forms written by Ameya Pitale. This book was released on 2019-05-07. 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.

Lectures on Modular Forms

1962-03-21 Education
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Release : 1962-03-21
Genre : Education
Kind : eBook
Book Rating : 951/5 ( reviews)

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Book Synopsis Lectures on Modular Forms by : Robert C. Gunning

Download or read book Lectures on Modular Forms written by Robert C. Gunning. This book was released on 1962-03-21. 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.

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