What question did this study set out to answer?

The aim is to analyze the asymptotic behavior and error term of the number of cyclic subgroups of the group Zℓ×Zm×Zn.

On the error term concerning the number of cyclic subgroups of Zℓ×Zm×ZnZ Z₌Z₍ with ℓmn ⩽ x

View Full Paper

Ask AI

Bookmark

Authors

Examines the asymptotic behavior of cyclic subgroups in Zℓ×Zm×Zn, highlighting implications for number theory.

The aim is to analyze the asymptotic behavior and error term of the number of cyclic subgroups of the group Zℓ×Zm×Zn.
Consider the asymptotic behavior of D3c(x) = ∑ℓmn ≤ x c(ℓ, m, n).
Utilize complex integration methods to derive an asymptotic formula.
Establish an upper bound for the integral mean-square of the error term.
Derived an asymptotic formula for the number of cyclic subgroups with respect to the variable x.
Obtained a precise upper bound for the error term in the asymptotic formula.

Li et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark