Estimates of Some Functions Over Primes without R.H.

Abstract

Some computations made about the Riemann Hypothesis and in particular, the verification that zeroes of zeta belong on the critical line and the extension of zero-free region are useful to get better effective estimates of number theory classical functions which are closely linked to zeta zeroes like psi(x), theta(x), pi(x) or the k-th prime number.

Cited by in corpus (3)

• Le plus grand facteur premier de la fonction de Landau
• On a conjecture of Pomerance
• Squarefree Integers And Extreme Values Of Some Arithmetic Functions