Lecture notes on nil-theta functions
Author(s)
Bibliographic Information
Lecture notes on nil-theta functions
（Regional conference series in mathematics, no. 34）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1977
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Note
"Expository lectures from the CBMS regional conference held at Cleveland State University, June 5-10, 1977."
Bibliography: p. 95-96
Description and Table of Contents
Description
This monograph consists of three chapters covering the following topics: Foundations, Bilinear forms and presentations of certain 2-step nilpotent Lie groups, Discrete subgroups of the Heisenberg group, The automorphism group of the Heisenberg group, Fundamental unitary representations of the Heisenberg group, The Fourier transform and the Weil-Brezin map, Distinguished subspaces and left action: Jacobi theta functions and the finite Fourier transform, Nil-theta functions and Jacobi-theta functions, and the algebra of the finite Fourier transform; Abelian varieties, nil-theta and theta functions.It includes: a general construction and algebraic foundations, Nil-theta functions associated with a positive definite H-morphism of an Abelian variety, and the relation between nil-theta and classical theta functions. In presenting the material, the author has attempted to lay a careful foundation and has stressed low-dimensional examples and special computations when proving general results by general techniques. This an expository piece of work, although some of the results are new.
Table of Contents
Foundations Jacobi theta functions and the finite Fourier transform Abelian varieties, nil-theta and theta functions Bibliography.
by "Nielsen BookData"