An improved upper bound for the argument of the Riemann zeta-function on the critical line

Trudgian, Timothy

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An improved upper bound for the argument of the Riemann zeta-function on the critical line

Date

2011-08-25

Authors

Trudgian, Timothy

Publisher

American Mathematical Society

Abstract

This paper concerns the function S(t), the argument of the Riemann zeta-function along the critical line. Improving on the method of Backlund, and taking into account the refinements of Rosser and McCurley it is proved that for sufficiently large t, |S(t)| ≤ 0.1013 log t. Theorem 2 makes the above result explicit, viz. it enables one to select values of a and b such that, for t>t0, |S(t)| ≤ a + b log t.