## Improvements to Turing’s method

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- by Timothy Trudgian PDF
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**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.## References

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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
- 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.
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2813359