5 papers
Some families of polynomials satisfying uniform boundedness for rational preperiodic points
Hector Pasten
We construct explicit non-isotrivial families of polynomials over satisfying uniform boundedness for their rational preperiodic points.
On the and the conjectures
Hector Pasten, Rocío Sepúlveda-Manzo
We revisit a subexponential bound for the conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove…
Szpiro's conjecture when the denominator of the -invariant is small
Hector Pasten
We prove Szpiro's conjecture for elliptic curves over the rationals having -invariant with denominator of logarithmic size with respect to its numerator.
On the arithmetic case of Vojta's conjecture with truncated counting functions
Hector Pasten
We prove a Diophantine approximation inequality for rational points in varieties of any dimension, in the direction of Vojta's conjecture with truncated counting functions. Our res…
Arithmetic derivatives through geometry of numbers
Hector Pasten
We define certain arithmetic derivatives on that respect the Leibniz rule, are additive for a chosen equation , and satisfy a suitable non-degeneracy condition.…