Congruences for Frobenius Partitions

Abstract

The partition functionp(n) has several celebrated congruence properties which reflect the action of the Hecke operators on certain holomorphic modular forms. In this article similar congruences are proved forc3(n), the number of generalized Frobenius partitions ofnwith 3 colors. We prove[formula]exept whenn=3TmandTm=m(m+1)/2 is themth triangular number, and[formula]Congruences (2) and (3) are analogous to Euler's pentagonal number theorem. These congruences are proved by constructing holomorphic modular forms which inherit related congruence properties which are verified computationally via Sturm's criterion.