Estimates of Some Functions Over Primes without R.H.

By Pierre Dusart. 2010

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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.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/85e188db48179c326354dd02f7269d7d89d30482