Explicit estimates for the Mertens function

Speaker: Nicol Leong

Date: Tue, Jun 18, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


We prove explicit estimates of $1/\zeta(s)$ of various orders, and use an improved version of the Perron formula to get explicit estimates for the Mertens function $M(x)$ of order $O(x)$, $O(x/\log^k x)$, and $O(x\log x exp(−\sqrt{\log{x}})$. These estimates are good for small, medium, and large ranges of $x$, respectively.

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