Improvements to Turing’s method

Trudgian, Timothy

doi:10.1090/S0025-5718-2011-02470-1

Improvements to Turing’s method
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Math. Comp. 80 (2011), 2259-2279 Request permission

Abstract:

This article improves the estimate of the size of the definite integral of $S(t)$, the argument of the Riemann zeta-function. The primary application of this improvement is Turing’s Method for the Riemann zeta-function. Analogous improvements are given for the arguments of Dirichlet $L$-functions and of Dedekind zeta-functions.

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