6 citations · 13 across the 9 of their papers we have counts for
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Statistical properties of Hecke correspondences
Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier
This paper studies the statistical properties of the dynamical system generated by a Hecke correspondence on the modular curve over and, for every prime number , ov…
Closing the gap around the essential minimum of height functions with linear programming
José Burgos Gil, Ricardo Menares, Binggang Qu +1
For many common height functions, it is notoriously hard to compute the essential minimum. Nevertheless there are two classical methods, one giving lower bounds and the other givin…
p-Adic distribution of CM points and Hecke orbits. II: Linnik equidistribution on the supersingular locus
Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier
For every prime number , this paper determines the asymptotic distribution of CM points on the moduli space of elliptic curves over . In stark contrast to the comp…
There are at most finitely many singular moduli that are S-units
Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier
We show that for every finite set of prime numbers S, there are at most finitely many singular moduli that are S-units. The key new ingredient is that for every prime number p, sin…
p-Adic distribution of CM points and Hecke orbits. I. Convergence towards the Gauss point
Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier
We study the asymptotic distribution of CM points on the moduli space of elliptic curves over , as the discriminant of the underlying endomorphism ring varies. In con…
The R-transform as a power map and its generalisations to higher degree
Alp Bassa, Ricardo Menares
We give iterative constructions for irreducible polynomials over F_q of degree nt^r for all nonnegative integers r, starting from irreducible polynomials of degree n. The iterative…
Enumeration of a special class of irreducible polynomials in characteristic 2
Alp Bassa, Ricardo Menares
A-polynomials were introduced by Meyn and play an important role in the iterative construction of high degree self-reciprocal irreducible polynomials over the field F_2, since they…
On the essential minimum of Faltings' height
José Burgos Gil, Ricardo Menares, Juan Rivera-Letelier
We study the essential minimum of the (stable) Faltings height on the moduli space of elliptic curves. We prove that, in contrast to the Weil height on a projective space and the N…
Strong modularity of reducible Galois representations
Nicolas Billerey, Ricardo Menares
In this paper, we call strongly modular those reducible semi-simple odd mod Galois representations for which the conclusion of the strongest form of Serre's original modularity…
On shifted primes with large prime factors and their products
Florian Luca, Ricardo Menares, Amalia Pizarro-Madariaga
We estimate from below the lower density of the set of prime numbers p such that p-1 has a prime factor of size at least p^c, where c lies in between 1/4 and 1/2. We also establish…
On the modularity of reducible mod l Galois representations
Nicolas Billerey, Ricardo Menares
We prove that every odd semisimple reducible (2-dimensional) mod l Galois representation arises from a cuspidal eigenform. In addition, we investigate the possible different types…
Equidistribution of Hecke points on the supersingular module
Ricardo Menares
For a fixed prime p, we consider the (finite) set of supersingular elliptic curves over . Hecke operators act on this set. We compute the asymptotic frequence wit…
Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves
Ricardo Menares
In the context of arithmetic surfaces, Bost defined a generalized Arithmetic Chow Group (ACG) using the Sobolev space L^2_1. We study the behavior of these groups under pull-back a…