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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A $q$-series identity and the arithmetic of Hurwitz zeta functions


Authors: Gwynneth H. Coogan and Ken Ono
Journal: Proc. Amer. Math. Soc. 131 (2003), 719-724
MSC (2000): Primary 11B65, 11M35
Published electronically: July 25, 2002
MathSciNet review: 1937408
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Abstract | References | Similar Articles | Additional Information

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

  • 1. G.E. Andrews, J. Jimenez-Urroz, K. Ono, $q$-series identities and values of certain $L-$functions, Duke Math. J. 108 (2001), 395-419.
  • 2. 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 (91j:33011)
  • 3. 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
Email: ono@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06649-2
PII: S 0002-9939(02)06649-2
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
Article copyright: © Copyright 2002 American Mathematical Society