Lehrbuch der Thetafunktionen

Krazer's impressive monograph on theta functions collects the properties and classic results about theta functions from the early part of the twentieth century. It is divided into three major parts. The first part covers general theta functions: their basic properties, representations of certain periodic functions in terms of theta functions, transformations of theta functions and complex multiplication. The second part describes the properties of theta functions with rational characteristic. The third part covers special theta functions, such as Abelian theta functions, hyperelliptic theta functions, and reducible Abelian integrals and their relationship to theta functions.