J. A. D. Reyna

collaborators

24 papers

math.NT2025

Asymptotic properties of zeros of Riemann zeta function

Juan Arias de Reyna, Yves Meyer

We try to define the sequence of zeros of the Riemann zeta function by an intrinsic property. Let $(z_{k})_{k \in N}$ be the sequence of nontrivial zeros of $I^¶ (s)$ with posi…

math.NT2024

On convergence of points to limiting processes, with an application to zeta zeros

Juan Arias de Reyna, Brad Rodgers

This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting poin…

math.NT2024

Simple bounds for the auxiliary function of Riemann

Juan Arias de Reyna

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

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{Ï…

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\{Ï^{-\frac{s}{2}}Î(s/2)f(s…

math.NT2024

Explicit van der Corput's $d$ -th derivative estimate

Juan Arias de Reyna

We give an explicit version for van der Corput's $d$ -th derivative estimate of exponential sums. $Theorem.$ Let $X$ , and $Y \in R$ be such that $\lfloor Y\rfloor>d…

Asymptotic properties of zeros of Riemann zeta function

On convergence of points to limiting processes, with an application to zeta zeros

Simple bounds for the auxiliary function of Riemann

A naive integral

Levinson Functions

Explicit van der Corput's d-th derivative estimate

Explicit van der Corput's $d$ -th derivative estimate