Abstract: Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo p for all primes p>3, which were conjectured earlier by the author. We extend Ono's method to handle the powers of 5, 7 and 13 congruences. We need the theory of weak Maass forms as well as certain classical modular equations for the Dedekind eta-function.

The url of this page is http://www.math.ufl.edu/~frank/abstracts/spt2.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Saturday, November 6, 2010.
Last update made Sat Nov 6 16:12:45 EDT 2010.

fgarvan@ufl.edu