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A  -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
Posted:
July 25, 2002
MathSciNet review:
1937408
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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.
- 1.
G.E. Andrews, J. Jimenez-Urroz, K. Ono,
 -series identities and values of certain  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.
- 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:
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
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
Article copyright:
© Copyright 2002 American Mathematical Society
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