Now showing items 1-10 of 10

  • Birch and Swinertonn-Dyer conjecture 

    Rivero Salgado, Óscar (Universitat Politècnica de Catalunya, 2016-01)
    Bachelor thesis
    Open Access
    Esta tesis tiene diversos objetivos: el primero de ellos es introducir temas básicos de teoría de números, empezando por la teoría algebraica (cuerpos de clases, teorema de Dirichlet...) y continuando por una exposición ...
  • Congruences between modular forms 

    Fernández Peña, Oriol (Universitat Politècnica de Catalunya, 2018-07)
    Master thesis
    Open Access
    This master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the ...
  • Modular curves and complex multiplication 

    Hernández Barrios, Víctor (Universitat Politècnica de Catalunya, 2018-07)
    Master thesis
    Open Access
    In this project we explore the connections between elliptic curves, modular curves and complex multiplication (CM). The main theorem of CM shows that the theory of CM for elliptic curves provides an explicit construction ...
  • No anul·lació de funcions L en valors crítics i resultats d'equidistribució en aritmètica 

    Arazo Marín, David (Universitat Politècnica de Catalunya, 2009-10)
    Master thesis
    Open Access
    L'objectiu del treball és revisar els principals resultats d'equidistribució en aritmètica. En primer terme es presenten i demostren el Teorema de densitat de Dirichlet i el Teorema de densitat de Chebotarev. La part central ...
  • 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 ...
  • Rational points on Atkin-Lehner quotients of Shimura curves 

    Vera Piquero, Carlos de (Universitat Politècnica de Catalunya, 2011)
    Master thesis
    Open Access
    Let X_B denote the Shimura curve defined by an indefinite rational quaternion division algebra B. By the work of Shimura, the curve X_B admits a canonical model over the field Q of rational numbers as a coarse moduli ...
  • 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 ...
  • Shimura varieties and Gross-Zagler formulae 

    Gutiérrez Terradillos, Armando (Universitat Politècnica de Catalunya, 2019-07)
    Master thesis
    Open Access
    Dissertation about the Gross-Zagier formulae and Shimura varieties.
  • Stark-Heegner points and p-adic L-functions 

    Casazza, Daniele (Universitat Politècnica de Catalunya, 2016-10-28)
    Doctoral thesis
    Open Access
    Covenantee:  Université de Bordeaux
    Let K|Q be a number field and let Z(K,s) be its associated complex L-function. The analytic class number formula relates special values of Z(K,s) with algebraic invariants of the field K itself. It admits a Galois equivariant ...
  • Stark's points and units 

    Rivero Salgado, Óscar (Universitat Politècnica de Catalunya, 2017-05)
    Master thesis
    Open Access
    El objetivo de este trabajo es el estudio de un análogo de la conjetura elíptica de Stark para unidades en cuerpos de números. Para ello, utilizamos el sistema de Euler de elementos de Beilinson-Flach y la posibilidad de ...