CBMS Regional Conference Series in Mathematics 1977; 96 pp; softcover Number: 34 Reprint/Revision History: reprinted 1984 ISBN10: 0821816845 ISBN13: 9780821816844 List Price: US$25 Member Price: US$20 All Individuals: US$20 Order Code: CBMS/34
 This monograph consists of three chapters covering the following topics: Foundations, (1) Bilinear forms and presentations of certain 2step nilpotent Lie groups, (2) Discrete subgroups of the Heisenberg group, (3) The automorphism group of the Heisenberg group, (4) Fundamental unitary representations of the Heisenberg group, (5) The Fourier transform and the WeilBrezin map, (6) Distinguished subspaces and left action: Jacobi theta functions and the finite Fourier transform, (1) Niltheta functions and Jacobitheta functions, (2) The algebra of the finite Fourier transform; Abelian varieties, niltheta and theta functions, (1) A general construction and algebraic foundations, (2) Niltheta functions associated with a positive definite Hmorphism of an Abelian variety, (3) The relation between niltheta and classical theta functions. In presenting the material, the author has attempted to lay a careful foundation and has stressed lowdimensional examples and special computations when proving general results by general techniques. This an expository piece of work, although some of the results are new. Readership Table of Contents  Foundations
 Jacobi theta functions and the finite Fourier transform
 Abelian varieties, niltheta and theta functions
 Bibliography
