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The number of finite non-isomorphic abelian groups in mean square.
Abstract : 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://hal.archives-ouvertes.fr/hal-01104704
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Monday, January 19, 2015 - 9:38:02 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Monday, April 20, 2015 - 10:25:22 AM
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Monday, January 19, 2015 - 9:38:02 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Monday, April 20, 2015 - 10:25:22 AM
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