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Statistic of zeros of Riemann auxiliary function
J. Arias de Reyna
We have computed all zeros of with . A total of 162215 zeros with 25 correct decimal digits. In this paper we offer some statistic ba…
Report on some papers related to the function found by Siegel in Riemann's posthumous papers
J. Arias de Reyna
In a letter to Weierstrass Riemann asserted that the number of zeros of on the critical line to height is approximately equal to the total number of zeros to th…
Simple bounds for the auxiliary function of Riemann
Juan Arias de Reyna
We give simple numerical bounds for , , , , for use in the numerical computation of these functions. The purpose of the paper is t…
A naive integral
Juan Arias de Reyna
In arXiv:2406.0243 two real functions and are defined, so that the Riemann-Siegel function is given as \[Z(t)=\mathop{\mathrm{Re}}\Bigl\{\frac{u(t)e^{\frac{πi…
Levinson Functions
Juan Arias de Reyna
Starting from some of Norman Levinson's results, we construct interesting examples of functions such that for , we have $Z(t)=2\Re\{π^{-\frac{s}{2}}Γ(s/2)f(s)\…
Explicit van der Corput's -th derivative estimate
Juan Arias de Reyna
We give an explicit version for van der Corput's -th derivative estimate of exponential sums. Let , and be such that $\lfloor Y\rfloor>d…