Research

Please see the corresponding journals for the final published versions. To avoid possible copyright problems, some of the preprints linked below are in arXiv and some are hosted in this web page.

• H. Pasten, Hilbert's tenth problem for rings of holomorphic functions of bounded order. Preprint (2024) (arXiv)

• H. Pasten, R. Sepulveda-Manzo, On the abc and the abcd conjectures. Preprint (2024) (arXiv)

• N. Garcia-Fritz, H. Pasten, Algebroid maps and hyperbolicity of symmetric powers. Preprint (2024) (arXiv)

• N. Garcia-Fritz, H. Pasten, X. Vidaux, Effectivity for existence of rational points is undecidable. Preprint (2023) (arXiv)

• H. Pasten, Szpiro's conjecture when the denominator of the j-invariant is small. Preprint (2023) (arXiv)

• H. Pasten, J. Silverman, Propagation of Zariski Dense Orbits. Preprint (2023) (arXiv)

• N. Garcia-Fritz, H. Pasten, T. Pheidas, Non-Diophantine sets in rings of functions. Preprint (2022) (arXiv)

• N. Garcia-Fritz, H. Pasten, A Diophantine definition of the constants in Q(z). Preprint (2022) (arXiv)

• H. Pasten, On the arithmetic case of Vojta's conjecture with truncated counting functions. Preprint (2022) (arXiv)

• H. Pasten, C. Salgado, Non-thin rank jumps for elliptic K3 surfaces.
Manuscripta Mathematica. To appear (2024)

• N. Garcia-Fritz, H. Pasten, Hilbert's tenth problem for lacunary entire functions of finite order. (arXiv)
Mathematical Logic Quarterly. To appear (2024)

• N. Garcia-Fritz, H. Pasten, A criterion for non-density of integral points. (arXiv)
Bulletin of the London Mathematical Society. To appear (2024)

• N. Garcia-Fritz, H. Pasten, Intersecting the torsion of elliptic curves. (arXiv)
Bulletin of the Australian Mathematical Society. To appear (2024)

• H. Pasten, The largest prime factor of n²+1 and improvements on subexponential ABC. (arXiv)
Inventiones Mathematicae. 236 (2024), no. 1, 373-385.

• H. Pasten, Shimura curves and the abc conjecture. (pdf)
Journal of Number Theory, Prime section. 254 (2024), 214-335.

• H. Pasten, A derivation of the infinitude of primes. (Link)
The American Mathematical Monthly. 131 (2024), no. 1, 66-73.

• J. Caro, H. Pasten, A Chabauty--Coleman bound for surfaces. (arXiv)
Inventiones Mathematicae. 234 (2023), no. 3, 1197-1250.

• H. Pasten, Definability and Arithmetic. (Link)
Notices of the AMS. 70 (2023), no. 9, 1385-1393.

• J. Caro, H. Pasten, On the fibres of an elliptic surface where the rank does not jump. (pdf)
Bulletin of the Australian Mathematical Society. 108 (2023), no. 2, 276-282.

• H. Pasten, Superficies elípticas y el décimo problema de Hilbert. (arXiv)
Revista Matemática: Teoría y Aplicaciones. 30 (2023), no. 1, 113-120.

• H. Pasten, On the Chevalley-Warning theorem when the degree equals the number of variables. (pdf)
Combinatorica. 42 (2022), suppl. 2, 1481-1486.

• H. Pasten, Arithmetic derivatives through geometry of numbers. (arXiv)
Canadian Mathematical Bulletin. 65 (2022), no. 4, 906-923.
This article was awarded the G. de B. Robinson Prize from the Canadian Math. Soc. (Link)

• D. Chompitaki, N. Garcia-Fritz, H. Pasten, T. Pheidas, X. Vidaux, The Diophantine problem for rings of exponential polynomials. (arXiv)
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. (5) 23 (2022), no. 4, 1625-1636.

• J. Caro, H. Pasten, Watkins's conjecture for elliptic curves with non-split multiplicative reduction. (pdf)
Proceedings of the American Mathematical Society. 150 (2022), no. 8, 3245-3251.

• H. Pasten, Notes on the DPRM property for listable structures. (arXiv)
Journal of Symbolic Logic. 87 (2022), no. 1, 273-312.

• H. Pasten, Remarks on the size of the Tamagawa product. (pdf)
Contemp. Math. 766, (2021) Geometry at the frontier. Symmetries and moduli spaces of algebraic varieties, 277-282.

• J. Esparza-Lozano, H. Pasten, A conjecture of Watkins for quadratic twists. (arXiv)
Proceedings of the American Mathematical Society, 149 (2021), no. 6, 2381-2385.

• N. Garcia-Fritz, H. Pasten, Elliptic curves with long arithmetic progressions have large rank. (pdf)
International Mathematics Research Notices, 2021, no. 10, 7394-7432.

• N. Garcia-Fritz, H. Pasten, Towards Hilbert's Tenth Problem for rings of integers through Iwasawa theory and Heegner points. (pdf)
Mathematische Annalen, (2020), 377(3), 989-1013.

• H. Pasten, Bivariate polynomial injections and elliptic curves. (pdf)
Selecta Mathematica, (2020), 26(2), 1-13.

• H. Pasten, Bounded ranks and Diophantine error terms. (pdf)
Mathematical Research Letters, 26 (2019), no. 5, 1559-1570.

• H. Pasten, L-functions, proximity functions, and Diophantine sets. (pdf)
Oberwolfach Reports, European Math. Soc. DOI: 10.4171/OWR/2016/49.

• R. Murty, H. Pasten, Elliptic curves, L-functions, and Hilbert's tenth problem. (pdf)
Journal of Number Theory, 182 (2018), 1-18.

• H. Pasten, Definability of Frobenius orbits and a result on rational distance sets. (pdf)
Monatshefte für Mathematik, 182 (2017), no. 1, 99-126.

• H. Pasten, J. Wang, GCD bounds for analytic functions. (pdf)
International Mathematics Research Notices, (2017), no. 1, 47-95.

• H. Pasten, X. Vidaux, Positive existential definability of multiplication from addition and the range of a polynomial. (pdf)
Israel Journal of Mathematics, 216 (2016), no. 1, 273-306.

• H. Pasten, C.-L. Sun, Multiplicative subgroups avoiding linear relations in finite fields and a local-global principle. (pdf)
Proceedings of the American Mathematical Society, 144 (2016), no. 6, 2361-2373.

• N. Garcia-Fritz, H. Pasten, Uniform positive existential interpretation of the integers in rings of entire functions of positive characteristic. (pdf)
Journal of Number Theory, 156 (2015), 368-393.

• H. Pasten, The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments. (pdf)
International Journal of Number Theory, 11 (2015) no. 3, 721-737.

• M. R. Murty, H. Pasten, Counting squarefree values of polynomials with error term. (pdf)
International Journal of Number Theory, 10 (2014) no. 7, 1743-1760.

• H. Pasten, J. Wang, Extensions of Büchi's higher powers problem to positive characteristic. (pdf)
International Mathematics Research Notices, Issue 11, 2015, Pages 3263-3297

• H. Pasten, T. Pheidas, X. Vidaux, Uniform existential interpretation of arithmetic in rings of functions of positive characteristic. (pdf)
Inventiones Mathematicae 196 (2014) no. 2 453-484.

• R. Murty, H. Pasten, Modular forms and effective diophantine approximation. (pdf)
Journal of Number Theory, 133 (2013), no. 11, 3739-3754.

• H. Pasten, Powerful values of polynomials and a conjecture of Vojta. (pdf)
Journal of Number Theory, 133 (2013), no. 9, 2964-2998.

• H. Pasten, Representation of squares by monic second degree polynomials in the field of p-adic meromorphic functions. (pdf)
Transactions of the American Mathematical Society, 364 (2012), no. 1, 417-446.

• H. Pasten, Büchi's problem in any power for finite fields.
Acta Arithmetica, 149 (2011), no. 1, 57-63.

• A. Escassut, H. Pasten, Büchi's problem for ultrametric meromorphic functions inside an open disk.
P-Adic Numbers Ultrametric Anal. Appl., 3 (2011), no. 2, 108-113.

• H. Pasten, T. Pheidas, X. Vidaux, A survey on Büchi's problem: new presentations and open problems.
POMI 377 (2010), Issledovaniya po Teorii Chisel. 10, 111--140, 243; translation in J. Math. Sci. (N. Y.) 171 (2010), no. 6, 765-781.

• H. Pasten, An extension of Büchi's problem for polynomial rings in zero characteristic.
Proceedings of the American Mathematical Society, 138 (2010), no. 5, 1549-1557.

Expository:

• Interview for The Hindu on the ABC conjecture (by S. Desikan). (link)

• H. Pasten, Un paseo por la modularidad, Joven Matematico, Pontificia Universidad Catolica de Chile 4: 25-39 (2012). (pdf)