On the error term concerning the number of cyclic subgroups of Zl × Zm × Zn with lmn≤slant x
Abstract
Let Zn denote the additive group of residue classes modulo n. Let c(l,m,n) denote the number of cyclic subgroups of Zl *Zm *Zn. For any x > 1, we consider the asymptotic behavior of D3c(x):= Σlmn≤ x c(l,m,n), obtain an asymptotic formula by complex method, and get an upper bound for the integral mean-square of the error term in that asymptotic formula.
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