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
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
Abstract:
We prove explicit estimates of 1/ζ(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/logkx), and O(xlogxexp(−√logx). These estimates are good for small, medium, and large ranges of x, respectively.
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