This is a list of my publications so far:
39. On transformation properties of hypergeometric motives and Diophantine equations.
Submitted pdf The code is available at this link
38. Hypergeometric Motives and the Generalized Fermat Equation.
with Franco Golfieri (with and appendix by Ariel Pacetti and Fernando Rodriguez Villegas
Submitted pdf
37. K-varieties and Galois representations.
with Enric Florit
Submitted pdf
36. On the 2-Selmer group of Jacobians of hyperelliptic curves.
with Daniel Barrera Salazar and Gonzalo Tornaría
Submitted pdf
35. On computing finite index subgroups of PSL(2,Z).
with Nicolás Mayorga Uruburu and Leandro Vendramin
To appearon Journal of Algebra and Its Applications pdf
34. Asymptotic results for the equations x 4+dy2=zp and x2+dy6=zp.
with Franco Golfieri and Lucas Villagra Torcomian
Submitted pdf
33. Quinary forms and Paramodular forms.
with Neil Dummigan, Gustavo Rama and Gonzalo Tornaría .
Mathematics of computations 93 (2024), n.348, 1805-1858 pdf
32. On the equation x 2+dy6=zp for square-free 1 ≤ d ≤ 20.
with Franco Golfieri and Lucas Villagra Torcomian
International Journal of Number Theory 19 (2023), no.5, 1129-1165. pdf.
The computations were done using the files mazur.mg, ellenberg.gp. The outputs (to certify the computations) are in this file.
31. A simplified proof of Serre's conjecture.
with Luis Dieulefait.
To appear in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. pdf
30. Q-curves, Hecke characters and some diophantine equations II.
with Lucas Villagra Torcomian.
Publicacions Matemàtiques 67(2023), no.2, 569-599.pdf
The scripts used in the article
include: RemoveCM.gp, magma scripts Mazur42p.mg, Case_d10.mg, Case_d11.mg, Case_d129.mg, Case_d19.mg, Case_d6.mg.
The script's outputs can be read on Outputs.txt and SageOutputs.txt. The tables were verified with the scripts table3.gp, table4.gp and table5.gp.
29. On Galois representations of superellitic curves..
With Angel Villanueva
Glasgow Mathematical Journal Vol. 65 Issue 2 (2023), 356-382 pdf
28. An exotic example of a tensor product of a CM elliptic curve and a weight $1$ form..
To appear in the Revista de la Unión Matemática Argentina pdf
27. Q-curves, Hecke characters and some diophantine
equations.
with Lucas Villagra Torcomian.
Math. Comp. 91 (2022), no. 338, 2817-2865 pdf
The scripts used in the article
include: Ellenberg.gp, magma scripts Mazur42p.mg, Mazur26p.mg, Eq1d5.mg, Eq1d6.mg, Eq1d7.mg, Eq2d5.mg, Eq2d6.mg and Eq2d7.mg.
The script's outputs can be read on OutputsEq1.txt and OutputsEq2.txt
26. On 2-Selmer groups and quadratic twists of elliptic curves.
with Daniel Barrera Salazar and Gonzalo Tornaría.
Math. Res. Lett. 28 (2021), no. 6, 1633-1659 pdf
25. On rational Bianchi newforms and abelian surfaces with quaternionic multiplication.
with John Cremona, Lassina Dembélé, Ciaran Schembri and John Voight.
Arithmetic geometry, number theory, and computation, 343-363, Simons Symp., Springer, Cham, 2021 pdf
24. On the number of Galois orbits of newforms.
with Luis Dieulefait and Paganiotis Tsaknias.
Jounal of the European Mathematical Society, Volume 23 Number 8 (2021) 2833-2860 pdf
23. On the paramodularity of typical abelian surfaces.
with Armand Brumer, Cris Poor, Gonzalo Tornaría, John Voight, and David S. Yuen.
Algebra and Number Theory, Volume 13 Number 5 (2019) 1145-1195 pdf
22. Anticyclotomic p-adic L-functions for additive reduction primes.
with Daniel Kohen.
Comptes Rendus Mathematique 356, Issue 10 (2018) 973-983 pdf Published
21. On Elliptic Curves of prime power conductor over imaginary quadratic fields with class number one.
with John Cremona.
Proceedings of the London Mathematical Society 118, Issue 5 (2019) 1245-1276 pdf
20. Non-paritious Hilbert modular forms.
with David Loeffler and Lassina Dembélé.
Mathematische Zeitschrift 292, Issue 1-2 (2019) 361-385.pdf Published
19. On Heegner points for primes of additive reduction ramifying in the base field.
with Daniel Kohen (and an appendix by Marc Masdeu);
Trans. of the AMS 370 (2018) 911-926.pdf
18. Theta Lifts of Bianchi Modular Forms and Applications to
Paramodularity.
with Tobias Berger, Lassina Dembele and
Mehmet Haluk Sengun;
Journal of the London
Mathematical Society 92 (2015) 353-370. pdf Published
17. Heegner Points on Cartan non-split curves.
with Daniel Kohen;
Canadian Journal of Mathematics 68 (2016) 422-444. pdf
16. Congruences between modular forms modulo prime powers.
with Maximiliano Camporino;
Revista Matemática Iberoamericana Volume 34 Issue 4 (2018), 1609-1643. pdf
For the example section, here are the files CongruencesRoutines.gp and E17a1example.txt and its output (at my home computer with the timings) E17a1example.output.txt
15. Connectedness of Hecke Algebras and the Rayuela conjecture: a path to functoriality and modularity.
with Luis Dieulefait.
Arithmetic and geometry, 193216, London Math. Soc. Lecture Note Ser., 420, Cambridge University Press (2015) pdf
14. Hecke and Sturm bounds for Hilbert modular forms over real
quadratic fields
with José Ignacio Burgos Gil
Math. Comp. 86 (2017), 1527-1552. pdf
13. Computing ideal classes representatives in quaternion algebras
with Nicolás Sirolli
Math. Comp. (2014). pdf
12. On the change of root numbers under twisting and applications
Proceedings of the AMS 141 (2013) n.8. pdf
11. Modularity of the Consani-Scholten quintic
with Luis Dieulefait and Matthias Schuett (and an appendix with Jose Burgos Gil)
Documenta Mathematica 17 (2012). pdf.
10. Shimura correspondence for level $p^2$ and the central values
of L-series II
with Gonzalo Tornaría
International Journal of Number Theory Vol. 10, N. 07 (2014) 1595-1635 pdf.
9. Proving Modularity for a given elliptic
curve over an imaginary quadratic field
with Luis Dieulefait and Lucio Guerberoff
Math. Comp. 79 N. 270 (2010) pdf.
A new version of the code (Novembre 2018) is available here which works over any number field, using the improvements due to Mok. The input only requires the field and the coefficients of the elliptic curve.
8. Shimura Correspondence and Central values of twisted
L-series
Proceedings of the "Segundas Jornadas de Teoría
de Números" pdf,
ISBN: 978-84-612-8007-0.
7. Computing central values of twisted L-series, the case of
composite levels
with Gonzalo Tornaría
Exp. Math. 17
N. 4 (2008) pdf.
6. On the embedding problem for 2^+S_ 4 representations
Math. Comp. 76 N. 260 (2007)
pdf.
5. Shimura Correspondance for level p^2 and the central values of
L-series
with Gonzalo Tornaría
Journal of Number
Theory 124 N. 2 (2007) pdf.
4. Newton-Hensel Interpolation Lifting
with
Martín Avendaño and Teresa Krick.
Found. of Comp. Math. 6 (1) 2006 pdf.
3. Examples of Shimura Correspondance for level p^2 and real
quadratic twists
with Gonzalo Tornaría
Ranks of elliptic curves and random matrix theory, pp. 289-314. pdf.
2. A formula for the central value of certain Hecke L-series (my
Ph.D. thesis).
Journal of Number Theory 113 (2005) dvi.
1. Computing Modular Forms of level p^2
with Fernando Rodriguez Villegas,
Math. Comp. 74 (2005) dvi.
My Ph.D. thesis at the University of Texas at Austin
pdf.
You can find some Pari/GP
scripts in the web page CNT.
Unpublished works:
Preimages for the Shimura map on Hilbert modular forms with Nicolás Sirolli (survey article). pdf
Course notes:
Formas automorfas: formas de Hilbert (notes from AGRA II, 2015). pdf
Representaciones de Galois (notes from AGRA III, 2018, with Luis Dieulefait and Fernando Rodriguez-Villetas). pdf