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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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On the quintuple product identity
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by Hershel M. Farkas and Irwin Kra PDF
Proc. Amer. Math. Soc. 127 (1999), 771-778 Request permission

Abstract:

In this note we present a new proof of the quintuple product identity which is based on our study of $k^{th}$ order theta functions with characteristics and the identities they satisfy. In this context the quintuple product identity is another example of an identity which when phrased in terms of theta functions, rather than infinite products and sums, has a simpler form and is much less mysterious.
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Additional Information
  • Hershel M. Farkas
  • Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
  • Email: farkas@math.huji.ac.il
  • Irwin Kra
  • Affiliation: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794
  • MR Author ID: 105975
  • Email: irwin@math.sunysb.edu
  • Received by editor(s): June 17, 1997
  • Additional Notes: The second authorโ€™s research was supported in part by NSF Grant DMS 9500557. The first authorโ€™s research was supported in part by the Gabriella and Paul Rosenbaum Foundation and the Edmund Landau Center for Research in Mathematical Analysis sponsored by the Minerva Foundation Germany. Both authors were supported in part by a US-Israel BSF Grant 95-348.
  • Communicated by: Dennis A. Hejhal
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 771-778
  • MSC (1991): Primary 30F30, 11F03; Secondary 30B99, 14H05, 05A30
  • DOI: https://doi.org/10.1090/S0002-9939-99-04791-7
  • MathSciNet review: 1487364