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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Theta functions of indefinite quadratic forms over real number fields
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by Olav K. Richter PDF
Proc. Amer. Math. Soc. 128 (2000), 701-708 Request permission

Abstract:

We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.
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Additional Information
  • Olav K. Richter
  • Affiliation: Department of Mathematics, University of California, San Diego, California 92093-0112
  • Address at time of publication: Department of Mathematics, University of California, Santa Cruz, California 95064
  • ORCID: 0000-0003-3886-0893
  • Email: richter@euclid.ucsd.edu, richter@math.ucsc.edu
  • Received by editor(s): April 29, 1998
  • Published electronically: September 27, 1999
  • Communicated by: Dennis A. Hejhal
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 701-708
  • MSC (1991): Primary 11F41; Secondary 11F27
  • DOI: https://doi.org/10.1090/S0002-9939-99-05619-1
  • MathSciNet review: 1706997