DE Reyna

activity

20242026

collaborators

5 papers

math.HO2026

Riemann and the logarithmic derivatives of zeta

J. Arias de Reyna

In one of his posthumous papers, conserved in GÃ¶ttingen, Riemann considers the derivatives of $lo g I^¶ (s)$ at the point $1/2$ , giving explicit values for them. Around 2010 we share…

math.NT2025

Explicit formula and quasicrystal definition

J. Arias de Reyna

We show that the Riemann hypothesis is true if and only if the measure $I^¼ = - n = 1 \sum \infty \frac{I ^ ( n )}{n} (I^´_{l o g n} + I^´_{- l o g n}) + 2 cosh (x /2) d x$ is a tempered distr…

math.NT2024

Statistic of zeros of Riemann auxiliary function

J. Arias de Reyna

We have computed all zeros $I^^{2} + i I^^{3}$ of $R (s)$ with $0 < I^^{3} < 215946.3$ . A total of 162215 zeros with 25 correct decimal digits. In this paper we offer some statistic…

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 $I^¶ (s)$ on the critical line to height $T$ is approximately equal to the total number of zeros to t…

math.HO2024

Riemann's auxiliary Function. Basic Results

J. Arias de Reyna

We give the definition, main properties and integral expressions of the auxiliary function of Riemann $R (s)$ . For example we prove $$Ï^{-s/2}Î(s/2)\mathop{\mat…

Riemann and the logarithmic derivatives of zeta

Explicit formula and quasicrystal definition

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

Riemann's auxiliary Function. Basic Results

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