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November 2008 A remark on the Möbius function
Jerzy Kaczorowski
Funct. Approx. Comment. Math. 39(1): 61-70 (November 2008). DOI: 10.7169/facm/1229696554

Abstract

It is proved that for every positive $B$ there exist real numbers $0=a_0<a_1<\ldots <a_N=1$ and $ \max_{1\leq j\leq N} (a_{j-1}/a_j)\leq\theta<1$ such that $$\limsup_{x\to\infty} \frac{1}{\sqrt{x}}\sum_{j=1}^N\sum_{\theta a_j x<n\leq a_j x} \mu(n) \geq B$$ and $$\liminf_{x\to\infty}\frac{1}{\sqrt{x}}\sum_{j=1}^N\sum_{\theta a_j x<n\leq a_j x} \mu(n)\leq -B,$$ where $\mu(n)$ denotes the Möbius function.

Citation

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Jerzy Kaczorowski. "A remark on the Möbius function." Funct. Approx. Comment. Math. 39 (1) 61 - 70, November 2008. https://doi.org/10.7169/facm/1229696554

Information

Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1228.11149
MathSciNet: MR2490088
Digital Object Identifier: 10.7169/facm/1229696554

Subjects:
Primary: 11N25
Secondary: 11M26, 11N37

Rights: Copyright © 2008 Adam Mickiewicz University

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Vol.39 • No. 1 • November 2008
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