Introductory Lectures on Siegel Modular Forms

ISBN-13: 9780521350525 / Angielski / Twarda / 1990 / 176 str.

Helmut Klingen; B. Bollobas; W. Fulton

Opis

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.

Recenzje

"...an excellent introduction to the subject of Siegel modular forms written by an expert and can be recommended highly as a first text in the subject." Mathematical Reviews

Spis treści

Preface; 1. The modular group; 2. Basic facts on modular forms; 3. Large weights; 4. Small weights; 5. Modular functions; 6. Dirichlet series; Bibliography; Index.