DE Reyna

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20242026

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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…

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

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