### Recent Submissions

• #### On the Elliptic Stark Conjecture in higher weight ﻿

(2020-01-01)
Article
Open Access
We study the special values of the triple product p-adic L-function constructed by Darmon and Rotger at all classical points outside the region of interpolation. We propose conjectural formulas for these values that can ...
• #### On some classes of irreducible polynomials ﻿

(2020-07)
Article
Restricted access - publisher's policy
One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irreducible factors. The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results ...
• #### Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N ﻿

(Multidisciplinary Digital Publishing Institute (MDPI), 2020-11-27)
Article
Open Access
In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to ...
• #### On rigid analytic uniformizations of Jacobians of Shimura curves ﻿

(2012)
Article
Open Access
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed ...
• #### The right-generators descendant of a numerical semigroup ﻿

(2020-01-01)
Article
Open Access
For a numerical semigroup, we encode the set of primitive elements that are larger than its Frobenius number and show how to produce in a fast way the corresponding sets for its children in the semigroup tree. This allows ...
• #### On the elliptic Stark conjecture at primes of multiplicative reduction ﻿

(2019-01-01)
Article
Open Access
In [DLR], Darmon, Lauder, and Rotger formulated a p-adic elliptic Stark conjecture for the twist of an elliptic curve E/Q by the self-dual tensor product ¿ ¿ of two odd and two-dimensional Artin representations. These ...
• #### CM-points and lattice counting on arithmetic compact Riemann surfaces ﻿

(2020-07)
Article
Open Access
Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the ...
• #### "Les matemàtiques i la vida" al Museu del Suro de Palafrugell ﻿

(Societat Catalana de Matemàtiques (SCM), 2019-07)
Article
Open Access
• #### Beilinson-Flach elements, Stark units and p-adic iterated integrals ﻿

(2019-08-14)
Article
Open Access
We study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in ...
• #### On the Galois embedding problem associated to the universal central extension of the alternating group of degree 6 ﻿

(2013)
Article
Open Access
We obtain an explicit expression for the obstruction to the solvability of the Galois embedding problem associated to the universal central extension of the alternating group of degree 6.
• #### Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field ﻿

(2018-07-01)
Article
Open Access
Let A/Q be an abelian variety of dimension g = 1 that is isogenous over Q to Eg, where E is an elliptic curve. If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition ...
• #### Del Pezzo surfaces over finite fields and their Frobenius traces ﻿

(2019-07)
Article
Open Access
Let S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases ...