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January 2007 Explicit estimates for summatory functions linked to the Möbius $\mu$-function
Henri Cohen, Francois Dress, Mahomed El Marraki
Funct. Approx. Comment. Math. 37(1): 51-63 (January 2007). DOI: 10.7169/facm/1229618741

Abstract

Let $M(x)$ be the summatory function of the Möbius function and $R(x)$ be the remainder term for the number of squarefree integers up to $x$. In this paper, we prove the explicit bounds $|M(x)|<x/4345$ for $x\ge 2160535$ and $|R(x)|\le 0.02767\sqrt x$ for $x\ge 438653$. These bounds are considerably better than preceding bounds of the same type and can be used to improve Schoenfeld type estimates.

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Henri Cohen. Francois Dress. Mahomed El Marraki. "Explicit estimates for summatory functions linked to the Möbius $\mu$-function." Funct. Approx. Comment. Math. 37 (1) 51 - 63, January 2007. https://doi.org/10.7169/facm/1229618741

Information

Published: January 2007
First available in Project Euclid: 18 December 2008

zbMATH: 1230.11118
MathSciNet: MR2357309
Digital Object Identifier: 10.7169/facm/1229618741

Subjects:
Primary: 11N37
Secondary: 11Y35, 11Y70

Rights: Copyright © 2007 Adam Mickiewicz University

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Vol.37 • No. 1 • January 2007
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