On some sums involving the counting function of non-isomorphic abelian groups

2022/04/06 by Fan, Haihong, Zhai, Wenguang
#11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2204.02576

Abstract

Let a(n) denote the number of non-isomorphic abelian groups with n elements. In 1991 Ivić proved an asymptotic formula of the sum ∑_{n≤ x} a(n+ a(n)). In this paper, we will prove a sharper asymptotic formula for this sum.

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