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Author : Yoshiyuki Kitaoka
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:
Author : Hans Maaß
Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 817/5 ( reviews)
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. This book was released on 2006-11-15. 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.
Author : Anatolij N. Andrianov
Release : 1987
Genre : Mathematics
Kind : eBook
Book Rating : 416/5 ( reviews)
Book Synopsis Quadratic Forms and Hecke Operators by : Anatolij N. Andrianov
Download or read book Quadratic Forms and Hecke Operators written by Anatolij N. Andrianov. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt: The numerous explicit formulae of the classical theory of quadratic forms revealed remarkable multiplicative properties of the numbers of integral representations of integers by positive definite integral quadratic forms. These properties were explained by the original theory of Hecke operators. As regards the integral representations of quadratic forms in more than one variable by quadratic forms, no multiplicative properties were known at that time, and so there was nothing to explain. However, the idea of Hecke operators was so natural and attractive that soon attempts were made to cultivate it in the neighbouring field of modular forms of several variables. The approach has proved to be fruitful; in particular, a number of multiplicative properties of integral representations of quadratic forms by quadratic forms were eventually discovered. By now the theory has reached a certain maturity, and the time has come to give an up-to-date report in a concise form, in order to provide a solid ground for further development. The purpose of this book is to present in the form of a self-contained text-book the contemporary state of the theory of Hecke operators on the spaces of hoi om orphic modular forms of integral weight (the Siegel modular forms) for congruence subgroups of integral symplectic groups. The book can also be used for an initial study of modular forms of one or several variables and theta-series of positive definite integral quadratic forms.
Author : Helmut Klingen
Release : 2008-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 091/5 ( reviews)
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.
Author : Ameya Pitale
Release : 2019-05-07
Genre : Mathematics
Kind : eBook
Book Rating : 753/5 ( reviews)
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.
