4 citations · 4 across the 7 of their papers we have counts for
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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…
Effectivity for existence of rational points is undecidable
Natalia Garcia-Fritz, Hector Pasten, Xavier Vidaux
The analogue of Hilbert's tenth problem over asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as o…
Superficies elípticas y el décimo problema de Hilbert
Hector Pasten
A negative solution to Hilbert's tenth problem for the ring of integers of a number field would follow if were Diophantine in . Denef and Lipshitz conje…
Uniform positive existential interpretation of the integers in rings of entire functions of positive characteristic
Natalia Garcia-Fritz, Hector Pasten
We prove a negative solution to the analogue of Hilbert's tenth problem for rings of one variable non-Archimedean entire functions in any characteristic. In the positive characteri…