Improved asymptotics for moments of reciprocal sums for partitions into distinct parts

Abstract

In this paper we strongly improve asymptotics for $s_1\left(n\right)$ (respectively $s_2\left(n\right)$) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of n into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not possess product expansions.