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March 2018 Improved explicit bounds for some functions of prime numbers
Sadegh Nazardonyavi
Funct. Approx. Comment. Math. 58(1): 7-22 (March 2018). DOI: 10.7169/facm/1547

Abstract

Using recent explicit asymptotic zero--free region and computations of zeros of the Riemann zeta function, obtained by Mossinghoff & Trudgian and Gourdon, respectively, we give an improvement for estimates of some functions related to distribution of primes, such as prime counting function, intervals containing at least one prime, Chebyshev's $\psi$ and $\vartheta$ functions.

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Sadegh Nazardonyavi. "Improved explicit bounds for some functions of prime numbers." Funct. Approx. Comment. Math. 58 (1) 7 - 22, March 2018. https://doi.org/10.7169/facm/1547

Information

Published: March 2018
First available in Project Euclid: 24 March 2018

zbMATH: 06924912
MathSciNet: MR3780030
Digital Object Identifier: 10.7169/facm/1547

Subjects:
Primary: 11A41
Secondary: 11K65, 11M26, 11N05

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.58 • No. 1 • March 2018
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