The number of finite non-isomorphic abelian groups in mean square.

Aleksandar Ivić

doi:10.46298/hrj.1986.117

Aleksandar Ivić - The number of finite non-isomorphic abelian groups in mean square.

hrj:117 - Hardy-Ramanujan Journal, January 1, 1986, Volume 9 -1986 - https://doi.org/10.46298/hrj.1986.117

The number of finite non-isomorphic abelian groups in mean square.Article

Authors: Aleksandar Ivić ¹

1 Katedra Matematike

Let $\Delta(x)=\sum_{n\leq x}a(n)-\sum_{j=1}^6 c_jx^{1/j}$ denote the error term in the abelian group problem. Using zeta-function methods it is proved that

$\int_1^X\Delta^2(x)\,dx~<\!\!<~ X^{39/29} \log^2X$ where the exponent

$39/29=1.344827\ldots$ is close to the best possible exponent

$4/3$ in this problem.

https://doi.org/10.46298/hrj.1986.117

Source: HAL:hal-01104704v1

Volume: Volume 9 -1986

Published on: January 1, 1986

Imported on: March 3, 2015

Keywords: mean square estimates,power moments of the zeta-function.,number of non-isomorphic abelian groups,[MATH]Mathematics [math]

Bibliographic References

1 Document citing this article

Share and export

Consultation statistics

This page has been seen 239 times.

This article's PDF has been downloaded 416 times.