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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Heisenberg manifolds and theta functions


Author: R. Tolimieri
Journal: Trans. Amer. Math. Soc. 239 (1978), 293-319
MSC: Primary 22E25; Secondary 14K25, 33A75, 43A85
DOI: https://doi.org/10.1090/S0002-9947-1978-0487050-7
MathSciNet review: 487050
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Abstract: The algebraic structure of the $(2n + 1)$-dimensional Heisenberg group naturally induces a special class of differential operators whose solutions $(Df = 0)$ are related to classical theta function theory.


References [Enhancements On Off] (What's this?)

  • L. Auslander and J. Brezin, Translation-invariant subspaces in $L^{2}$ of a compact nilmanifold. I, Invent. Math. 20 (1973), 1–14. MR 322100, DOI https://doi.org/10.1007/BF01405260
  • Jun-ichi Igusa, Theta functions, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 194. MR 0325625
  • Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
  • Serge Lang, Introduction to algebraic and abelian functions, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1972. MR 0327780
  • A. I. Mal′cev, On a class of homogeneous spaces, Izvestiya Akad. Nauk. SSSR. Ser. Mat. 13 (1949), 9–32 (Russian). MR 0028842
  • O. T. O’Meara, Introduction to quadratic forms, Springer, Berlin, 1963. C. L. Siegel, Quadratic forms, Lectures on Math., no. 7, Tata Institute of Fundamental Research, Bombay, 1967.

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Article copyright: © Copyright 1978 American Mathematical Society