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 the modulus for partition related functions, we extend the modulo 32760 congruences of the first author for the function spt(n). We show that a normalized form of the generating function of spt(n) is an eigenform modulo 32 for the Hecke operators T(ℓ~2) for primes ℓ ≥5 with e=1,11,17,19 (mod 24), and an eigenform modulo 16 for ℓ = 13,23 (mod 24).