Sharper estimates for Chebyshev's functions $\vartheta$ and $\psi$

Abstract

In this article we present some improved results for Chebyshev's functions $\vartheta$ and $\psi$ using the new zero-free region obtained by H. Kadiri and the calculated the first $10^{13}$ zeros of the Riemann zeta function on the critical line by Xavier Gourdon. The methods in the proofs are similar to those of Rosser-Shoenfeld papers on this subject.

After finishing this article we realized that some of the theorems of this article was found by Pierre Dusart. In this article we give the proofs with more details. The proof essentially similar to those of Rosser and Shoenfeld papers in this area

References in corpus (1)

• Estimates of Some Functions Over Primes without R.H.