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arXiv:2105.06821 [math.NT]AbstractReferencesReviewsResources

Atkinson's formula for the mean square of $ζ(s)$ with an explicit error term

Aleksander Simonič, Valeriia V. Starichkova

Published 2021-05-14, updated 2021-05-27Version 2

We provide an explicit $O\left(\log^2{T}\right)$-term of the celebrated Atkinson's formula for the error term $E(T)$ of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate $E(T)\ll_{\varepsilon} T^{\frac{1}{3}+\varepsilon}$.

Comments: 41 pages, 1 figure, 2 tables
Categories: math.NT
Subjects: 11M06, 11N37, 11Y35
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