A note on the number of abelian groups of a given order
L\'aszl\'o T\'oth
TL;DR
This paper derives an asymptotic formula for the moments of the function counting non-isomorphic Abelian groups of a given order, improving previous results for the quadratic moment.
Contribution
It provides a new asymptotic formula for the power moments of the Abelian group count function, refining earlier quadratic moment estimates.
Findings
Asymptotic formula for power moments of a(n)
Improved quadratic moment estimate
Enhanced understanding of Abelian group distribution
Abstract
We point out an asymptotic formula for the power moments of the function , representing the number of non-isomorphic Abelian groups of order . For the quadratic moment this improves an earlier result due to L. Zhang, M. L\"u and W. Zhai.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Theories · History and Theory of Mathematics