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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A $q$-series identity and the arithmetic of Hurwitz zeta functions
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by Gwynneth H. Coogan and Ken Ono PDF
Proc. Amer. Math. Soc. 131 (2003), 719-724 Request permission

Abstract:

Using a single variable theta identity, which is similar to the Jacobi Triple Product identity, we produce the generating functions for values of certain expressions of Hurwitz zeta functions at non-positive integers.
References
  • G.E. Andrews, J. Jimenez-Urroz, K. Ono, $q$-series identities and values of certain $L-$functions, Duke Math. J. 108 (2001), 395–419.
  • Nathan J. Fine, Basic hypergeometric series and applications, Mathematical Surveys and Monographs, vol. 27, American Mathematical Society, Providence, RI, 1988. With a foreword by George E. Andrews. MR 956465, DOI 10.1090/surv/027
  • D. Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001), 945–960.
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Additional Information
  • Gwynneth H. Coogan
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: gwynneth@math.wisc.edu
  • Ken Ono
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 342109
  • Email: ono@math.wisc.edu
  • Received by editor(s): October 22, 2001
  • Published electronically: July 25, 2002
  • Additional Notes: The authors thank the National Science Foundation for their generous support. The second author also thanks the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation for their generous support
  • Communicated by: David E. Rohrlich
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 719-724
  • MSC (2000): Primary 11B65, 11M35
  • DOI: https://doi.org/10.1090/S0002-9939-02-06649-2
  • MathSciNet review: 1937408