J. Varona

activity

19952026

most citedHarmonic Analysis associated with a discrete Laplacian

85 citations · 282 across the 23 of their papers we have counts for

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8 papers · 1 filter

math.NT2023

The computation of $ζ (2 k)$ , $β (2 k + 1)$ and beyond by using telescoping series

Óscar Ciaurri, Luis M. Navas, Francisco J. Ruiz +1

We present some simple proofs of the well-known expressions for \[ ζ(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad β(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] w…

math.NT2023★ 7 cited

Three essays on Machin's type formulas

Armengol Gasull, Florian Luca, Juan L. Varona

We study three questions related to Machin's type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated $2$ -integers, that is va…

math.NT2021

On the Solution of the Equation $n = ak + b p_{k}$ by Means of an Iterative Method

Juan Luis Varona

For fixed positive integers $n$ , we study the solution of the equation $n = k + p_{k}$ , where $p_{k}$ denotes the $k$ th prime number, by means of the iterative method \[ k_{j+1} = π(n-…

math.NT2020

A Couple of Transcendental Prime-Representing Constants

Juan L. Varona

It is well known that the arithmetic nature of Mills' prime-representing constant is uncertain: we do not know if Mills' constant is a rational or irrational number. In the case of…

math.NT2020

Continued fractions for strong Engel series and Lüroth series with signs

Andrew N. W. Hone, Juan Luis Varona

An Engel series is a sum of reciprocals $\sum_{j \geq 1} 1/ x_{j}$ of a non-decreasing sequence of positive integers $x_{n}$ with the property that $x_{n}$ divides $x_{n + 1}$ for all $n\geq…

math.NT2018★ 10 cited

Continued fractions and irrationality exponents for modified Engel and Pierce series

Andrew N. W. Hone, Juan Luis Varona

An Engel series is a sum of reciprocals of a non-decreasing sequence $(x_{n})$ of positive integers, which is such that each term is divisible by the previous one, and a Pierce serie…

math.NT2012★ 16 cited

A simple computation of $ζ (2 k)$ by using Bernoulli polynomials and a telescoping series

Ó. Ciaurri, L. M. Navas, F. J. Ruiz +1

We present a new proof of Euler's formulas for $ζ (2 k)$ , where $k = 1, 2, 3, ...$ , which uses only the defining properties of the Bernoulli polynomials, obtaining the value of $ζ (2 k)$ …

math.NT2011★ 37 cited

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

Luis M. Navas, Francisco J. Ruiz, Juan L. Varona

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $B_{n} (x; λ)$ in detail. The starting point is their Fourier series on $[0, 1]$ which, it is shown,…

The computation of ζ(2k), β(2k+1) and beyond by using telescoping series