Improvements to Turing's Method II

preprint2014arXivOpen access

Abstract

Turing's method uses explicit bounds on ∣∫t1t2S(t) dt∣|\int_{t_{1}}^{t_{2}} S(t)\, dt|, where πS(t)πS(t) is the argument of the Riemann zeta-function. This article improves the bound on ∣∫t1t2S(t) dt∣|\int_{t_{1}}^{t_{2}} S(t)\, dt| given in an earlier paper by the author.

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