Lecture Notes on Nil-theta Functions (CBMS Regional Conference Series in Mathematics No. 34)

Lecture Notes on Nil-theta Functions (CBMS Regional Conference Series in Mathematics No. 34)

By: Louis Auslander (author)Paperback

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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.

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Contents

Foundations Jacobi theta functions and the finite Fourier transform Abelian varieties, nil-theta and theta functions Bibliography.

Product Details

  • publication date: 15/12/1977
  • ISBN13: 9780821816844
  • Format: Paperback
  • Number Of Pages: 96
  • ID: 9780821816844
  • ISBN10: 0821816845

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