マンフォード著・データ関数講義録ＩＩＩ Tata Lectures on Theta III (Modern Birkhäuser Classics) （1st ed. 1991. reprint 2007.）

Mumford, David

Birkhäuser（2007/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 202 p.
• 言語 ENG
• 商品コード 9780817645700
• DDC分類 510

基本説明

Originally published as volume 97 in the series: Progress in Mathematics. This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics.

Full Description

This volume is the third of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).

Contents

Heisenberg groups in general.- The real Heisenberg groups.- Finite Heisenberg groups and sections of line bundles on abelian varieties.- Adelic Heisenberg groups and towers of abelian varieties.- Algebraic theta functions.- Theta functions with quadratic forms.- Riemann's theta relation.- The metaplectic group and the full functional equation of ?.- Theta Functions in Spherical Harmonics.- The homogeneous coordinate ring of an abelian variety.