A new upper bound for |ζ(1+it)|

Authors

  • T. Trudgian ANU

Keywords:

Riemann zeta function, explicit bound, one line

Abstract

It is known that ζ(1+it)≪(logt)2/3 when t≫1. This paper provides a new explicit estimate |ζ(1+it)|≤34logt, for t≥3. This gives the best upper bound on |ζ(1+it)| for t≤102⋅105. 10.1017/S0004972713000415

Author Biography

T. Trudgian, ANU

Mathematical Sciences Institute ARC Early Career Research Fellow

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles
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