Recent Submissions

  • On the Elliptic Stark Conjecture in higher weight 

    Gatti, Francesca; Guitart Morales, Xavier (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 

    Gutiérrez Gutiérrez, Jaime; Jiménez Urroz, Jorge (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 

    Dieulefait, Luis Victor; Jiménez Urroz, Jorge (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 

    Longo, Matteo; Rotger Cerdà, Víctor; Vigni, Stefano (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 

    Bras Amorós, Maria; Fernández González, Julio (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 

    Casazza, Daniele; Rotger Cerdà, Víctor (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 

    Alsina Aubach, Montserrat; Chatzakos, Dimitrios (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 

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

    Rivero Salgado, Óscar; Rotger Cerdà, Víctor (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 

    Crespo, Teresa; Vela del Olmo, Maria Montserrat (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 

    Fite Naya, Francesc; Guitart Morales, Xavier (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 

    Banwait, Barinder; Fite Naya, Francesc; Loughran, Daniel (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 ...

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