J. A. de Reyna

collaborators

26 papers

math.HO2026

Riemann and the logarithmic derivatives of zeta

J. Arias de Reyna

In one of his posthumous papers, conserved in Göttingen, Riemann considers the derivatives of $lo g ζ (s)$ at the point $1/2$ , giving explicit values for them. Around 2010 we shared…

math.NT2024

Statistic of zeros of Riemann auxiliary function

J. Arias de Reyna

We have computed all zeros $β + iγ$ of $R (s)$ with $0 < γ < 215946.3$ . A total of 162215 zeros with 25 correct decimal digits. In this paper we offer some statistic ba…

math.NT2024

Report on some papers related to the function $R (s)$ found by Siegel in Riemann's posthumous papers

J. Arias de Reyna

In a letter to Weierstrass Riemann asserted that the number $N_{0} (T)$ of zeros of $ζ (s)$ on the critical line to height $T$ is approximately equal to the total number of zeros to th…

math.NT2024

Simple bounds for the auxiliary function of Riemann

Juan Arias de Reyna

We give simple numerical bounds for $ζ (s)$ , $ϑ (s)$ , $R (s)$ , $Z (t)$ , for use in the numerical computation of these functions. The purpose of the paper is t…

math.NT2024

A naive integral

Juan Arias de Reyna

In arXiv:2406.0243 two real functions $g (x, t)$ and $f (x, t)$ are defined, so that the Riemann-Siegel $Z$ function is given as \[Z(t)=\mathop{\mathrm{Re}}\Bigl\{\frac{u(t)e^{\frac{πi…

math.NT2024

Levinson Functions

Juan Arias de Reyna

Starting from some of Norman Levinson's results, we construct interesting examples of functions $f (s)$ such that for $s = \frac{1}{2} + i t$ , we have $Z(t)=2\Re\{π^{-\frac{s}{2}}Γ(s/2)f(s)\…

Riemann and the logarithmic derivatives of zeta

Statistic of zeros of Riemann auxiliary function

Report on some papers related to the function R(s) found by Siegel in Riemann's posthumous papers

Simple bounds for the auxiliary function of Riemann

A naive integral

Levinson Functions

Report on some papers related to the function $R (s)$ found by Siegel in Riemann's posthumous papers