2 citations · 2 across the 4 of their papers we have counts for
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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 -…
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…