New estimates for some functions defined over primes
Number Theory
2017-05-18 v2
Abstract
In this paper we first establish new explicit estimates for Chebyshev's -function. Applying these new estimates, we derive new upper and lower bounds for some functions defined over the prime numbers, for instance the prime counting function , which improve the currently best ones. Furthermore, we use the obtained estimates for the prime counting function to give two new results concerning the existence of prime numbers in short intervals.
Cite
@article{arxiv.1703.08032,
title = {New estimates for some functions defined over primes},
author = {Christian Axler},
journal= {arXiv preprint arXiv:1703.08032},
year = {2017}
}
Comments
14 pages, v2: minor changes (for instance, a smaller interval in Theorem 4.1 is obtained)