• An inverse Jacobian algorithm for Picard curves 

      Lario Loyo, Joan Carles; Somoza Henares, Anna; Vincent, Christelle (Springer, 2021-06-01)
      Article
      Accés obert
      We study the inverse Jacobian problem for the case of Picard curves over C. More precisely, we elaborate on an algorithm that, given a small period matrix O¿C3×3 corresponding to a principally polarized abelian threefold ...
    • Cropping Euler factors of modular L-functions 

      González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles (2013-09)
      Article
      Accés obert
      According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
    • Frobenius distribution for quotients of Fermat curves of prime exponent 

      Fité, Francesc; González Rovira, Josep; Lario Loyo, Joan Carles (2015-06-18)
      Article
      Accés obert
      Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as quotients of C by certain subgroups of ...
    • Galois: entre els radicals 

      Lario Loyo, Joan Carles (2012-10-03)
      Audiovisual
      Accés obert
    • Gauss i els polígons 

      Lario Loyo, Joan Carles (2006-02-15)
      Audiovisual
      Accés obert
      Per copsar el llegat de Gauss, cal tenir en compte què va fer, naturalment, però també què va deixar als altres per fer. En aquest article expositiu, mostrem aquest fet en el cas de la constructibilitat amb regle i ...
    • On elliptic Galois representations and genus-zero modular units 

      Fernández González, Julio; Lario Loyo, Joan Carles (2006-07-03)
      Article
      Accés obert
      Given an odd prime \,$p$\, and a representation $\varrho$\, of the absolute Galois group of a number field $k$ onto $\mathrm{PGL}_2(\mathbb{F}_p)$ with cyclotomic determinant, the moduli space of elliptic curves defined ...
    • Rational points on twists of X0(63) 

      Bruin, Nils; Fernández González, Julio; González i Rovira, Josep; Lario Loyo, Joan Carles (2006-02-07)
      Article
      Accés obert
      Let $\varrho\colon G_\mathbb{Q}\longrightarrow PGL_2(\mathbb{F}_p)$ be a Galois representation with cyclotomic determinant, and let $N>1$ be an integer that is square mod $p$. There exist two twisted modular curves ...
    • Satins, lattices, and extended Euclid's algorithm 

      Brunat Blay, Josep M.; Lario Loyo, Joan Carles (2021-01-01)
      Article
      Accés obert
      Motivated by the design of satins with draft of period m and step a, we draw our attention to the lattices L(m,a)=¿(1,a),(0,m)¿ where 1=a<m are integers with gcd(m,a)=1. We show that the extended Euclid's algorithm applied ...