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| Author | : Yoshiyuki Kitaoka |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 1986 |
| Genre | : Forms (Mathematics). |
| ISBN | : |
| Author | : Helmut Klingen |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2008-05-15 |
| Genre | : Mathematics |
| ISBN | : 9780521062091 |
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 | : Y. Kitaoka |
| Publisher | : |
| Total Pages | : 227 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Hans Maass |
| Publisher | : Springer |
| Total Pages | : 348 |
| Release | : 1971 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Ameya Pitale |
| Publisher | : Springer |
| Total Pages | : 138 |
| Release | : 2019-05-07 |
| Genre | : Mathematics |
| ISBN | : 3030156753 |
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.
| Author | : Carl Ludwig Siegel |
| Publisher | : |
| Total Pages | : 410 |
| Release | : 1967 |
| Genre | : Forms, Quadratic |
| ISBN | : |
| Author | : Hans Maass |
| Publisher | : |
| Total Pages | : 646 |
| Release | : 1954 |
| Genre | : Functions, Modular |
| ISBN | : |
| Author | : Ricardo Baeza |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 424 |
| Release | : 2009-08-14 |
| Genre | : Mathematics |
| ISBN | : 0821846485 |
This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.
| Author | : Jan Hendrik Bruinier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2008-02-10 |
| Genre | : Mathematics |
| ISBN | : 3540741194 |
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.
| Author | : Krishnaswami Alladi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2013-08-13 |
| Genre | : Mathematics |
| ISBN | : 1461474884 |
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
