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

Trudgian, Timothy


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.

CollectionsANU Research Publications
Date published: 2011-08-25
Type: Journal article
Source: Mathematics of Computation
DOI: 10.1090/S0025-5718-2011-02537-8


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