Recurrence and congruences for the smallest part function
Authors
Wei Wang
Abstract
Let be the number of smallest parts in the partitions of . In this paper, we give some generalized Euler-like recursive formulas for the function in terms of Hecke trace of values of special twisted quadratic Dirichlet series. As a corollary, we give a closed form expressions of the power series , , by Hecke traces for weight cusp forms on . We further establish an incongruence result for the function.
