8 citations · 17 across the 7 of their papers we have counts for
7 papers
Algorithms for determining integer complexity
J. Arias de Reyna, J. van de Lune
We present three algorithms to compute the complexity of all natural numbers . The first of them is a brute force algorithm, computing all these complexitie…
"How many 's are needed?" revisited
J. Arias de Reyna, J. van de Lune
We present a rigorous and relatively fast method for the computation of the "complexity" of a natural number (sequence A005245), and answer some "old and new" questions related to…
On the exact location of the non-trivial zeros of Riemann's zeta function
Juan Arias de Reyna, Jan van de Lune
In this paper we introduce the real valued real analytic function kappa(t) implicitly defined by exp(2 pi i kappa(t)) = -exp(-2 i theta(t)) * (zeta'(1/2-it)/zeta'(1/2+it)) and kapp…
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…
A note on the real part of the Riemann zeta-function
Juan Arias de Reyna, Richard P. Brent, Jan van de Lune
We consider the real part of the Riemann zeta-function in the half-plane . We show how to compute accurately the constant which…
Some bounds and limits in the theory of Riemann's zeta function
J. Arias de Reyna, J. van de Lune
For any real a>0 we determine the supremum of the real σ such that ζ(σ+it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different.} We also…
A glimpse inside the mathematical kitchen
Juan Arias-de-Reyna, Jan van de Lune
We prove the inequality sum_{k=1}^infty (-1)^{k+1} r^k cos(k*phi) (k+2)^{-1} < sum_{k=1}^infty(-1)^{k+1} r^k (k+2)^{-1} for 0 < r <= 1 and 0 < phi < pi. For the case r = 1 we give…