Now showing items 1-18 of 18

    • A study of visibility graphs for time series representations 

      Bergillos Varela, Carlos (Universitat Politècnica de Catalunya, 2020-06-22)
      Bachelor thesis
      Open Access
      En aquest projecte estudiem i presentem el camp dels grafs de visibilitat (visibility graphs) com una forma de representar i caracteritzar sèries temporals tal com va ser introduït per Lucas Lacasa et al. el 2008. Amb els ...
    • Arithmetic properties of non-hyperelliptic genus 3 curves 

      Lorenzo García, Elisa (Universitat Politècnica de Catalunya, 2014-09-10)
      Doctoral thesis
      Open Access
      This thesis explores the explicit computation of twists of curves. We develope an algorithm for computing the twists of a given curve assuming that its automorphism group is known. And in the particular case in which the ...
    • Computing congruences of modular forms and Galois representations modulo prime powers 

      Taixes Ventosa, Xavier; Wiese, Gabor (2010)
      Article
      Open Access
      This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime ...
    • Congruences between modular forms and lowering the level mod l^n 

      Dieulefait, Luis Victor; Taixes Ventosa, Xavier (2009)
      Article
      Open Access
      In this article we study the behavior of inertia groups for modular Galois mod ℓn representations and in some cases we give a generalization of Ribet’s lowering the level result.
    • Differential galois theory and non-integrability of planar polynomial vector fields 

      Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (2018-02-26)
      Article
      Restricted access - publisher's policy
      We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular ...
    • Equations of hyperelliptic Shimura curves 

      Molina Blanco, Santiago (2012)
      Article
      Open Access
      We describe a method for computing equations of hyperelliptic Shimura curves attached to indefinite quaternion algebras over Q and Atkin–Lehner quotients of them. It exploits Cerednik–Drinfeld 's non-archimedean uniformization ...
    • From Galois to Hopf Galois: theory and practice 

      Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Maria Montserrat (2015-09)
      Article
      Open Access
      Hopf Galois theory expands the classical Galois theory by con- sidering the Galois property in terms of the action of the group algebra k [ G ] on K/k and then replacing it by the action of a Hopf algebra. We review the ...
    • Galoisian approach to supersymmetric quantum mechanics 

      Acosta Humánez, Primitivo Belén (Universitat Politècnica de Catalunya, 2009-07-02)
      Doctoral thesis
      Open Access
      Esta tesis versa sobre el punto de vista desde la Teoría de Galois Diferencial hacia la mecánica cuántica supersimétrica. El objeto principal considerado aquí es la ecuación deSchrödinger estacionaria no relativista, ...
    • Generic Galois extensions for SL_2(F_5) over Q 

      Plans Berenguer, Bernat (Mathematical Publishing, 2007)
      Article
      Open Access
      Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of ...
    • On elliptic Galois representations and genus-zero modular units 

      Fernández González, Julio; Lario Loyo, Joan Carles (2006-07-03)
      Article
      Open Access
      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 ...
    • On fields of definition of torsion points of elliptic curves with complex multiplication 

      Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (2011-06)
      Article
      Open Access
      For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...
    • On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory 

      Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-01-12)
      External research report
      Open Access
      We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ...
    • Ordinary CM forms and local Galois representations 

      Castellà Cabello, Francesc (Universitat Politècnica de Catalunya, 2009-07)
      Master thesis
      Open Access
      "The p-adic Galois representation \rho_f attached to a p-ordinary newform f of weight k>1 is known to be reducible when restricted to a decomposition group D_p at p. Ralph Greenberg asked for a characterization of those f ...
    • Polynomials in finite geometry 

      Ball, Simeon Michael; Blokhuis, Aart (Università degli studi di Napoli. Dipartimento di Matematica, 1999-11-01)
      Part of book or chapter of book
      Open Access
    • Rational points on Shimura curves and Galois representations 

      Vera Piquero, Carlos de (Universitat Politècnica de Catalunya, 2014-11-07)
      Doctoral thesis
      Open Access
      This thesis explores one of the essential arithmetical and diophantine properties of Shimura curves and their Atkin-Lehner quotients: the existence of rational points on these families of curves over both number fields and ...
    • Rational points on twists of X0(63) 

      Bruin, Nils; Fernández González, Julio; González i Rovira, Josep; Lario Loyo, Joan Carles (2006-02-07)
      Article
      Open Access
      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 ...
    • The Hopf Galois property in subfield lattices 

      Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Maria Montserrat (2016-01-01)
      Article
      Open Access
      Let K/k be a finite separable extension, n its degree and (K) over tilde /k its Galois closure. For n <= 5, Greither and Pareigis show that all Hopf Galois extensions are either Galois or almost classically Galois and they ...
    • The polynomial method in Galois geometries 

      Ball, Simeon Michael (Nova Science Publishers, 2012)
      Part of book or chapter of book
      Restricted access - publisher's policy
      The polynomial method refers to the application of polynomials to combinatorial problems. The method is particularly effective for Galois geometries and a number of problems and conjectures have been solved using the ...