Now showing items 1-10 of 10

    • Automorphic SL2-periods and the subconvexity problem for GL2xGL3 

      Pal, Aprameyo; Vera Piquero, Carlos de (2020-01-09)
      External research report
      Open Access
      We prove a new (conditional) result towards the subconvexity problem for certain automorphic L-functions for GL2xGL3. This follows from the computation of new SL2-period integrals associated with newforms f and g of even ...
    • CM cycles on Kuga-Sato varieties over Shimura curves and Selmer groups 

      Elias, Yara; Vera Piquero, Carlos de (2018)
      Article
      Open Access
      Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve ...
    • Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture 

      Longo, Matteo; Rotger Cerdà, Víctor; Vera Piquero, Carlos de (2018-01-01)
      Article
      Open Access
      We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternionic orders. We address several questions ...
    • Local points on Shimura coverings of Shimura curves at bad reduction primes 

      Vera Piquero, Carlos de (2016)
      Article
      Open Access
      Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D>1. For each prime l|D, there is a natural cyclic Galois covering of Shimura curves XD,l → XD constructed by ...
    • p-adic families of d-th Shintani liftings 

      Casazza, Daniele; Vera Piquero, Carlos de (2019-12-11)
      External research report
      Open Access
      In this note we give a detailed construction of a Lambda-adic d-th Shintani lifting. We derive a p-adic version of Kohnen's formula relating Fourier coefficients of half-integral weight modular forms and special values of ...
    • Pullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 L-series 

      Pal, Aprameyo; Vera Piquero, Carlos de (2019)
      Article
      Open Access
      We prove an explicit central value formula for a family of complex L-series of degree 6 for GL2 × GL3 which arise as factors of certain Garret–Rankin triple product L-series associated with modular forms. Our result ...
    • Punts racionals en corbes de Shimura sobre cossos quadr atics imaginaris 

      Vera Piquero, Carlos de (2012)
      External research report
      Open Access
      Mem oria presentada al Premi Évariste Galois de la SCM, 49a convocat òria
    • 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 ...
    • The Shimura covering of a Shimura curve: automorphisms and étale subcoverings 

      Vera Piquero, Carlos de (2013-10)
      Article
      Restricted access - publisher's policy
      Let XDXD be the Shimura curve associated with an indefinite rational quaternion algebra of discriminant D, and let p be a prime dividing D. In their investigations on the arithmetic of XD, Jordan and Skorobogatov introduced ...