Theta Functions

Theta Functions
Author :
Publisher : Springer Science & Business Media
Total Pages : 246
Release :
ISBN-10 : 9783642653155
ISBN-13 : 3642653154
Rating : 4/5 (154 Downloads)

Book Synopsis Theta Functions by : Jun-ichi Igusa

Download or read book Theta Functions written by Jun-ichi Igusa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e., after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I.A.S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W.L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C


Theta Functions Related Books

Theta Functions
Language: en
Pages: 246
Authors: Jun-ichi Igusa
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We sha
A Brief Introduction to Theta Functions
Language: en
Pages: 100
Authors: Richard Bellman
Categories: Mathematics
Type: BOOK - Published: 2013-01-01 - Publisher: Courier Corporation

DOWNLOAD EBOOK

Originally published: New York: Rinehart and Winston, 1961.
Theta Functions on Riemann Surfaces
Language: en
Pages: 142
Authors: J. D. Fay
Categories: Mathematics
Type: BOOK - Published: 2006-11-15 - Publisher: Springer

DOWNLOAD EBOOK

These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topi
Ramanujan's Theta Functions
Language: en
Pages: 696
Authors: Shaun Cooper
Categories: Mathematics
Type: BOOK - Published: 2017-06-12 - Publisher: Springer

DOWNLOAD EBOOK

Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory
Conformal Blocks, Generalized Theta Functions and the Verlinde Formula
Language: en
Pages: 539
Authors: Shrawan Kumar
Categories: Mathematics
Type: BOOK - Published: 2021-11-25 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.