Convolution congruences for the partition function
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- by Sharon Anne Garthwaite PDF
- Proc. Amer. Math. Soc. 135 (2007), 13-20 Request permission
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 $\ell \geq 5$.References
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Additional Information
- Sharon Anne Garthwaite
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- Email: garthwai@math.wisc.edu
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 13-20
- MSC (2000): Primary 11P83; Secondary 11F11
- DOI: https://doi.org/10.1090/S0002-9939-06-08443-7
- MathSciNet review: 2280169