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math.NT2012★ 1 cited
On the sign of the real part of the Riemann zeta-function
Juan Arias de Reyna, Richard P. Brent, Jan van de Lune
We consider the distribution of on fixed lines , and in particular the density \[d(σ) = \lim_{T \rightarrow +\infty} \frac{1}{2T} |\{t \in [-T,+T]: |\argζ…
math.NT2012★ 7 cited
The n-th prime asymptotically
Juan Arias de Reyna, Toulisse Jeremy
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement o…