An improved explicit estimate for ζ(1/2+it)ζ(1/2+it)

preprint2022arXivOpen access

Abstract

An explicit subconvex bound for the Riemann zeta function ζ(s)ζ(s) on the critical line s=1/2+its=1/2+it is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction in that lemma, we recover and improve the record explicit bound for ∣ζ(1/2+it)∣|ζ(1/2 + it)|.

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