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Mathematics of Computation

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Improvements to Turing’s method

Author: Timothy Trudgian
Journal: Math. Comp. 80 (2011), 2259-2279
MSC (2010): Primary 11M06, 11R42; Secondary 11M26
Published electronically: March 1, 2011
MathSciNet review: 2813359
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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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Additional Information

Timothy Trudgian
Affiliation: Mathematical Institute, University of Oxford, OX1 3LB England
Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, University Drive W, Lethbridge, AB, T1K 3M4, Canada
MR Author ID: 909247

Keywords: Turing’s method, Riemann zeta-function, Dirichlet $L$-functions, Dedekind zeta-functions
Received by editor(s): December 9, 2009
Received by editor(s) in revised form: August 2, 2010
Published electronically: March 1, 2011
Additional Notes: I wish to acknowledge the financial support of the General Sir John Monash Foundation, and Merton College, Oxford.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.