Hector Pasten
Pontifical Catholic University of Chile
44 Papers
108 Citations
Hector Pasten is an academic researcher from Pontifical Catholic University of Chile. The author has contributed to research in topics: Elliptic curve & Conjecture. The author has an hindex of 8, co-authored 38 publications. Previous affiliations of Hector Pasten include Princeton University & Harvard University.
Chat about Author
Papers
A survey on Büchi’s problem: new presentations and open problems
TL;DR: In a commutative ring with a unit, a Buchi sequence is a sequence such that the second difference of the sequence of its squares is the constant sequence (2).
28
The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments
TL;DR: In this article, Tao and Ziegler gave an asymptotic estimate for the number of square-free values of a polynomial at prime arguments on the ABC conjecture.
23
Towards Hilbert's Tenth Problem for rings of integers through Iwasawa theory and Heegner points
TL;DR: For a positive proportion of primes p and q, it was shown in this paper that ρ is Diophantine in the ring of integers of ρ for ρ = ρ ≥ 0.
17
Definability of Frobenius orbits and a result on rational distance sets
TL;DR: In this paper, it was shown that the first order theory of (possibly transcendental) meromorphic functions of positive characteristic (p>2) is undecidable and that the abc conjecture implies a solution to the Erdos-Ulam problem on rational distance sets.
16
An extension of Büchi’s problem for polynomial rings in zero characteristic
Hector Pasten
- 29 Dec 2009
TL;DR: In this paper, a strong form of the n-squares problem over polynomial rings with characteristic zero constant field was shown to be NP-hard, and it was shown that for all r ≥ 2 there exists an integer M = M(r) depending only on r such that, if z 1, z 2,..., z M are distinct elements of F and we have polynomials f,g,x 1,x 2,x 3,x 4,x 5,x 6,x M ∈ F[t], with some x