Hector Pasten

activity

20142026

most citedIntersecting the torsion of elliptic curves

1 citations · 1 across the 18 of their papers we have counts for

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Showing 2019Show all

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math.NT2019

Elliptic curves with long arithmetic progressions have large rank

Natalia Garcia-Fritz, Hector Pasten

For any family of elliptic curves over the rational numbers with fixed $j$ -invariant, we prove that the existence of a long sequence of rational points whose $x$ -coordinates form a…

math.NT2019

Towards Hilbert's Tenth Problem for rings of integers through Iwasawa theory and Heegner points

Natalia Garcia-Fritz, Hector Pasten

For a positive proportion of primes $p$ and $q$ , we prove that $Z$ is Diophantine in the ring of integers of $Q (3 p, - q)$ . This provides a new and e…