title: The spt-function of Andrews.
abstract: Recently, Andrews introduced the function s(n) = spt(n) which counts the number of smallest parts among the integer partitions of n. We show that its generating function satisfies an identity analogous to Ramanujan's mock theta identities. As a consequence, we are able to completely determine the parity of s(n). Using another type of identity, one based on Hecke operators, we obtain a complete multiplicative theory for s(n) modulo 3. These congruences confirm unpublished conjectures of Garvan and Sellers. Our methods generalize to all integral moduli.
authors.affiliation: Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.
authors.forename: Amanda
authors.initials: A
authors.lastname: Folsom
authors.forename: Ken
authors.initials: K
authors.lastname: Ono