$\ell$-adic properties of smallest parts functions

Details $\ell$-adic properties of smallest parts functions $\ell$-adic properties of smallest parts functions

2010-11-28

arxiv.org/abs/1011.6079v1

Mathematics

Number Theory

Scientific paper

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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