New bounds for $\psi (x)$
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- by Laura Faber and Habiba Kadiri PDF
- Math. Comp. 84 (2015), 1339-1357 Request permission
Corrigendum: Math. Comp. 87 (2018), 1451-1455.
Abstract:
In this article we provide new explicit Chebyshev bounds for the prime counting function $\psi (x)$. The proof relies on two new arguments: smoothing the prime counting function which allows one to generalize the previous approaches, and a new explicit zero density estimate for the zeros of the Riemann zeta function.References
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Additional Information
- Laura Faber
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada
- MR Author ID: 1097651
- Email: laura.faber2@uleth.ca
- Habiba Kadiri
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada
- MR Author ID: 760548
- Email: habiba.kadiri@uleth.ca
- Received by editor(s): July 18, 2013
- Received by editor(s) in revised form: September 9, 2013
- Published electronically: October 21, 2014
- Additional Notes: The first author was funded by a Chinook Research Award.
The second author was funded by ULRF Fund 13222.
The authors’ calculations were done on the University of Lethbridge Number Theory Group Eudoxus machine, supported by an NSERC RTI grant. - © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 1339-1357
- MSC (2010): Primary 11M06, 11M26
- DOI: https://doi.org/10.1090/S0025-5718-2014-02886-X
- MathSciNet review: 3315511