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arXiv · 1011.6079

$\ell$-adic properties of smallest parts functions

Scott Ahlgren·Kathrin Bringmann·Jeremy Lovejoy
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Abstract

We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on $\ell$-adic properties of certain modular forms and mock modular forms of weight $3/2$ with respect to the Hecke operators $T(\ell^{2m})$.

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Scott Ahlgren, Kathrin Bringmann, Jeremy Lovejoy. 2010-11-28. $\ell$-adic properties of smallest parts functions. https://arxiv.org/abs/1011.6079

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