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A formula and a congruence for Ramanujan's  -function
Author:
Matthew Papanikolas
Journal:
Proc. Amer. Math. Soc. 134 (2006), 333-341
MSC (2000):
Primary 11F30; Secondary 11F33, 11T24, 33C99
Posted:
June 14, 2005
MathSciNet review:
2175999
Full-text PDF Free Access
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Additional Information
Abstract: We determine formulas for Ramanujan's  -function and for the coefficients of modular forms on  in terms of finite field  -hypergeometric functions. Using these formulas we obtain a new congruence of  .
References
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Additional Information
Matthew Papanikolas
Affiliation:
Department of Mathematics, Texas A{&}M University, College Station, Texas 77843
Email:
map@math.tamu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08029-9
PII:
S 0002-9939(05)08029-9
Received by editor(s):
April 27, 2004
Received by editor(s) in revised form:
September 9, 2004
Posted:
June 14, 2005
Additional Notes:
This research was supported by NSF grant DMS-0340812 and NSA grant MDA904-03-1-0019
Communicated by:
Wen-Ching Winnie Li
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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