Improvements to Turing’s method
Author:
Timothy Trudgian
Journal:
Math. Comp. 80 (2011), 2259-2279
MSC (2010):
Primary 11M06, 11R42; Secondary 11M26
DOI:
https://doi.org/10.1090/S0025-5718-2011-02470-1
Published electronically:
March 1, 2011
MathSciNet review:
2813359
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Email:
tim.trudgian@uleth.ca
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.
