WEEKLY ACTIVITIES

On the Mertens function
Speaker: Dang Vu Giang

Time: 9h00, Friday, October 14, 2016
Location: Room 109, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract:Let $M (x)= \sum\limits_{n\le x} {\mu(n)}$ denote the Mertens function. For any fixed $\epsilon>0$ we prove that \[ \frac{\ln\ln w}{\ln^{1+\epsilon}w} \int_1^wM(x)\left[\frac wx\right]\frac{dx}x\to 0 \] as $w\to\infty$. Here, $[a]$ denotes the integer part of $a$.

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