Research:
(Please see the corresponding journals for the final published versions.)

H. Pasten, Shimura curves and the abc conjecture. Preprint (2017). (pdf)

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

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

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

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

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

H. Pasten, C.-L. Sun, Multiplicative subgroups avoiding linear relations in finite fields and a local-global principle. Proc. Amer. Math. Soc. 144 (2016), no. 6, 2361-2373. (pdf)

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

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

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

H. Pasten, J. Wang, Extensions of Büchi's higher powers problem to positive characteristic. International Mathematics Research Notices (2014) (published online first on March 2014). (pdf)

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

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

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

H. Pasten, Representation of squares by monic second degree polynomials in the field of p-adic meromorphic functions. Trans. Amer. Math. Soc. 364 (2012), no. 1, 417-446. (pdf)

H. Pasten, Büchi's problem in any power for finite fields. Acta Arith. 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. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (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. Proc. Amer. Math. Soc. 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)