Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Convolution congruences for the partition function

Author: Sharon Anne Garthwaite
Journal: Proc. Amer. Math. Soc. 135 (2007), 13-20
MSC (2000): Primary 11P83; Secondary 11F11
Published electronically: June 19, 2006
MathSciNet review: 2280169
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Abstract: Ahlgren and Boylan recently proved the uniqueness of the Ramanujan congruences for the primes $ 5$, $ 7$, and $ 11$ by using the modularity of a certain partition function. Here we use their result to find universal congruences, of a different type, which hold for the partition function modulo all primes $ \ell\geq 5$.

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Sharon Anne Garthwaite
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Received by editor(s): July 5, 2005
Received by editor(s) in revised form: July 25, 2005
Published electronically: June 19, 2006
Additional Notes: This research was supported by the University of Wisconsin Madison NSF VIGRE program
Communicated by: Ken Ono
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.