## A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive

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- by Yannick Saouter, Timothy Trudgian and Patrick Demichel PDF
- Math. Comp.
**84**(2015), 2433-2446 Request permission

## Abstract:

We consider the least number $x$ for which a change of sign of $\pi (x)-\mathrm {li}(x)$ occurs. First, we consider modifications of Lehmanβs method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first $x$ for which the difference is positive. Third, we use numerical computations to improve the final result.## References

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## Additional Information

**Yannick Saouter**- Affiliation: Institut Telecom Brest, Department Informatique, CS 83818, 29238 Brest, Cedex 3 France
- Email: Yannick.Saouter@enst-bretagne.fr
**Timothy Trudgian**- Affiliation: The Australian National University, Mathematical Sciences Institute, Building 27, ACTON, ACT 0200 Australia
- MR Author ID: 909247
- Email: timothy.trudgian@anu.edu.au
**Patrick Demichel**- Affiliation: Hewlett-Packard France, 91947 Les Ulis, Cedex France
- Email: patrick.demichel@hp.com
- Received by editor(s): June 11, 2013
- Received by editor(s) in revised form: December 4, 2013
- Published electronically: February 12, 2015
- Additional Notes: The second author was supported in part by ARC Grant DE120100173.
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp.
**84**(2015), 2433-2446 - MSC (2010): Primary 11-04, 11A15, 11M26, 11Y11, 11Y35
- DOI: https://doi.org/10.1090/S0025-5718-2015-02930-5
- MathSciNet review: 3356033