arXiv subjects

Orlando Galdames-Bravo

Publications and source records attributed to Orlando Galdames-Bravo.

2 recordsLinked to original sources

arXiv2025

On the verification of a Nicolas inequality

Nicolas inequality we deal can be written as \begin{equation}\label{Nicineq} e^γ\log\log N_x < \dfrac{N_x}{φ(N_x)}\,, \end{equation} where $x\ge 2$, $N_x$ denotes the product of the primes less or equal than $x$, $γ$ is the Euler constant and $φ$ is the Euler totient function. We see that verification of such an inequality depends on the sign of the big-O function in the Mertens estimate for the sum of reciprocals of primes that. Then we analyze the sign of such an error term.

math.NT↗

arXiv2019

First integral by means of the uniformization over the torus

The uniformization of a direction field was defined by Finn (in 1973) for the classification of certain differential operators. In the present note we recover the idea of uniformization in order to generalize it and apply it to the existence of first integrals. Roughly speaking, we say that a plane vector field $X$ on $D\subset\mathbb{R}^2$ is uniformizable over $T^2$ (the torus) if there is a constant vector field $Z$ on $Δ\subset T^2$ and a diffeomorphism $ψ\colon D\to Δ\subset T^2$ such that $dψ\circ X = Z\circψ$.

math.DS↗