2 citations · 3 across the 5 of their papers we have counts for
6 papers
Improved bounds for Szpiro's conjecture
Hector Pasten
In the direction of Szpiro's conjecture for all elliptic curves over , the current best bound is where is the absolute value of the minimal…
Power-saving bounds for Thue--Mahler and Mordell equations
Hector Pasten
We prove a new effective bound for cubic Thue--Mahler equations with power-saving dependence on the regulator. This has some applications. First, we improve Stark's bound $\log \ma…
On the greatest prime factor of polynomial values and subexponential Szpiro in families
José Cuevas Barrientos, Hector Pasten
Combining a modular approach to the conjecture developed by the second author with the classical method of linear forms in logarithms, we obtain improved unconditional bounds…
A conjecture of Watkins for quadratic twists
Jose A. Esparza-Lozano, Hector Pasten
Watkins conjectured that for an elliptic curve over of Mordell-Weil rank , the modular degree of is divisible by . If has non-trivial rational -…
Shimura curves and the abc conjecture
Hector Pasten
We develop a general framework to study Szpiro's conjecture and the conjecture by means of Shimura curves and their maps to elliptic curves, introducing new techniques that a…
Representation of powers by polynomials over function fields and a problem of Logic
Hector Pasten
We solve a generalization of Büchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where thi…