Convolution congruences for the partition function

Garthwaite, Sharon

doi:10.1090/S0002-9939-06-08443-7

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 $\ell \geq 5$.

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