Hecke-type congruences for Andrews' spt-function modulo 16 and 32

摘要

Inspired by recent congruences by Andersen with varying powers of 2 in themodulus for partition related functions, we extend the modulo 32760 congruencesof the first author for the function spt(n). We show that a normalized form ofthe generating function of spt(n) is an eigenform modulo 32 for the Heckeoperators T(l^2) for primes l >= 5 with l congruent to 1, 11, 17, 19 (mod 24),and an eigenform modulo 16 for l congruent to? 13, 23 (mod 24).