Hecke's Theory of Modular Forms and Dirichlet Series

Drawing upon Hecke's notes and his own lectures, Berndt (mathematics, U. of Illinois at Urbana-Champaign) and co-author Knopp (Mathematics, Temple U.) present new and important developments of recent years in the theory of correspondence. They begin by describing Hecke's main correspondence theorem and establish a couple of useful lemmas, then work through a fundamental region. They closely work through three cases, in which the lemma is greater than two, less than two, and equal to two, and describe Bochner's generalization of the main correspondence theorem of Hecke with related results and present identities equivalent to the functional equation and to the modular relation. They provide a comprehensive bibliography and useful index. Annotation c2008 Book News, Inc., Portland, OR (booknews.com)