Ricardo Menares


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Preprints

(with José Burgos Gil, Binggang Qu and Martín Sombra) Closing the gap around the essential minimum of height functions with linear programming. axiv:2601.18978

(with Sebastián Herrero and Juan Rivera-Letelier) p-adic distribution of CM points and Hecke orbits. II. Linnik equidistribution on the supersingular locus. arxiv:2102.04865


Publications

10) (with Alp Bassa) The R-transform as power map and its generalisations to higher degree. Finite Fields Appl. 102 (2025), published version  arXiv:1909.02608

9) (with Sebastián Herrero and Juan Rivera-Letelier) There are at most finitely many singular moduli that are S-units. Compositio Math. 160 (2024), no.4, 732-770. arxiv:2102.05041

8) (with Sebastián Herrero and Juan Rivera-Letelier) p-adic distribution of CM points and Hecke orbits. I. Convergence towards the Gauss point. Algebra & Number Theory. 14 (2020), no. 5, 1239-1290. arXiv:2002.03232

7) (with Alp Bassa) Enumeration of a special class of irreducible polynomials in characteristic 2. Acta Arith. 194 (2020), no. 1, 51–57. arXiv:1905.08345

6) (with José Burgos Gil and Juan Rivera-Letelier) On the essential minimum of Faltings' height. Math. Comp. 87 (2018), no. 313, 2425–2459. arXiv:1609.00071 Slides

5) (with Nicolas Billerey) Strong modularity of reducible Galois representations. Trans. Amer. Math. Soc. 370 (2018), no. 2, 967–986. arXiv:1604.01173

4) (with Nicolas Billerey) On the modularity of reducible mod l Galois representations. Math. Res. Lett. 23 (2016), no. 1, 15–41. arXiv:1309.3717

3) (with Florian Luca and Amalia Pizarro-Madariaga) On shifted primes with large prime factors and their products. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 1, 39–47. arXiv:1311.2527

2) Equidistribution of Hecke points on the supersingular module. Proc. Amer. Math. Soc. 140 (2012), no. 8, 2687–2691. arXiv:1303.1320

1) Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves.  Manuscripta Math. 136 (2011), no. 3-4, 501–543 arxiv: 0911.0546

0) Ph. D. Thesis: Nombres d'intersection arithmétiques et opérateurs de Hecke sur les courbes modulaires. tel-00360171

Other mathematical texts

(with José Burgos Gil) Equidistribución, teoría del potencial y aplicaciones aritméticas. Publicaciones Matemáticas del Uruguay, Vol. 18, Diciembre 2023 (Notes for a course in AGRA III school. July 2018).
We cover elementary concepts from potential theory and apply them to prove the classical Fekete-Szegö theorem, including a slight refinement showing equidistribution in the case of capacity one. We also cover Bilu's theorem on equidistribution of points with small height in tori. These notes are mostly self-contained.

Construcciones geométricas sólo con compás, Revista del profesor de Matemáticas, Año 8, número 1.

Tate Algebras (2011)
These notes are a compilation of facts and proofs about Tate algebras.


Grants

april 2021-march 2025 : Fondecyt Regular 1211858 (PI)
april 2017-march 2021 : Fondecyt Regular 1171329 (PI)
2017-2019 : ECOS-CONICYT (member)
2016: PEPS, CNRS (member, PI: Nicolas Billerey)
2015-2016 : Proyectos internos PUCV 24.750/2015, 124.756/2016 (PI)
2014 : MEC 80130064, CONICYT (sponsor)
2012-2014: Proyecto interno PUCV 124.734/2012 (PI)
2011-2014 : Fondecyt Iniciación 11110225 (PI)