Nick Andersen

Affiliation: University of Illinois

Email: nandrsn4@illinois.edu

Title Of Talk: Hecke-type congruences for two smallest parts functions

URL: http://arxiv.org/pdf/1209.4009v1.pdf

Abstract: We prove infinitely many congruences modulo $3$, $5$, and powers of 2 for the overpartition function $\bar{p}(n)$ and two smallest parts functions: $\overline{spt1}(n)$ for overpartitions and $M2spt(n)$ for partitions without repeated odd parts. These resemble the Hecke-type congruences found by Atkin for the partition function $p(n)$ in 1966 and Garvan for the smallest parts function $spt(n)$ in 2010. The proofs depend on congruences between the generating functions for $\bar{p}(n)$, $\overline{spt1}(n)$, and $M2spt(n)$ and eigenforms for the half-integral weight Hecke operator $T(\ell^{2})$.

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