Ricardo Menares
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Preprint
(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. To appear in: Finite Fields Appl. 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)