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A -series identity and the arithmetic of Hurwitz zeta functions

Author(s): Gwynneth H. Coogan; Ken Ono
Journal: Proc. Amer. Math. Soc. 131 (2003), 719-724.
MSC (2000): Primary 11B65, 11M35
Posted: July 25, 2002
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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:

1.: G.E. Andrews, J. Jimenez-Urroz, K. Ono, -series identities and values of certain functions, Duke Math. J. 108 (2001), 395-419.
2.: N. Fine, Basic hypergeometric series and applications, Math. Surv. and Mono. 27, Amer. Math. Soc. 1988. MR 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: 10.1090/S0002-9939-02-06649-2
PII: S 0002-9939(02)06649-2
Received by editor(s): October 22, 2001
Posted: 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 of article: Copyright 2002, American Mathematical Society


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