Tata Lectures on Theta II

Abstract

This book is the first volume (consisting of two chapters) of a planned treatise (containing four chapters) on theta functions and their applications to number theory, algebraic geometry and certain nonlinear differential equations. The first chapter ("Introduction and motivation: theta functions in one variable'') does not use algebraic geometry. Here the point of departure is the elementary theory of functions of one complex variable, but the second chapter ("Basic results on theta functions of several variables'') requires some algebraic geometry for comprehension, although this chapter does contain all the definitions of the notions used, and the author asserts that both chapters "assume only a knowledge of elementary classical analysis''.