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Publications

 

Papers accepted for publication

  • A. Betina. Les variétés de Hecke-Hilbert aux points classiques de poids paralléle 1, to appear in J. Théor. Nombres Bordeaux.
  • A. Betina, E. Lecouturier. On the p-adic periods of the modular curve X(Γ_0(p)∩Γ(2)), to appear in Trans. Amer. Math. Soc.
  • D. Casazza, V. Rotger. Stark points and Hida-Rankin p-adic L-functions, to appear in the Ramanujar J. Math.
  • M. Longo, V. Rotger, C. de Vera-Piquero, Heegner points on Hijigata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture, to appear in Publicacions Matematiques.
  • Somoza, A; Lario, J-C. The Sato-Tate conjecture for a Picard curve with Complex Multiplication, To appear in: the proceedings of the conference in honor of Prof. Momose, Contemporary Mathematics.

2017

2016

    2015

      2014

        2013

        2012

        2011

        2010

        2009

        2008

        I. Goldbring, M. Masdeu, Bezout domains and elliptic curves. Communications in Algebra 36, no. 12 (2008), 4492-4499.

        J. Conde, J. Gimbert, J. González, J. M. Miret, and R. Moreno, Nonexistence of almost Moore digraphs of diameter three. Electron. J. Combin. 15 (2008), no. 1, Research Paper 87, 14.

        J. Fernández, A moduli approach to quadratic Q-curves realizing projective mod p Galois representations. Rev. Mat. Iberoamericana 28 (2008), no. 1, 1--30.

        J. González, On cubic factors of j-invariants of quadratic Q-curves of prime degree. J. Number Theory 128 (2008), no. 2, 377--389.

        J. Jiménez, Almost prime orders of CM elliptic curves modulo p. ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings, LNCS Vol. 5011, pp 74--87.

        A. Kontogeorgis, V. Rotger, On abelian automorphism groups of Mumford curves, Bull. London Math. Soc. 40 (2008) no. 3, 353-362.

        A. Kontogeorgis, V. Rotger, On the non-existence of exceptional automorphisms on Shimura curves. Bull. London Math. Soc. 40 (2008) no. 3, 363-374.

        V. Rotger, Which quaternion algebras act on a modular abelian variety? Math. Res. Lett. 15 (2008), no. 2, 251--263.

        2007

        N. Bruin, J. Fernández, J. González, J.-C. Lario, Rational points on twists of X0(63). Acta Arith. 126 (2007), no. 4, 361--385.

        G. Cardona, J. Quer, Curves of genus 2 with group of automorphisms isomorphic to D8 or D12. Trans. Amer. Math. Soc. 359 (2007), no. 6, 2831--2849.

        J. Fernández, J. González, J.-C. Lario, Plane quartic twists of X(5,3). Canadian Math. Bull. 50 (2007), 196--205.

        J. Fernández, J.-C. Lario, On elliptic Galois representations and genus-zero modular units. J. Théor. Nombres Bordeaux. 19 (2007), 141--165.

        J. Guàrdia, Thetanullwerte: From periods to good equations. Proceedings of the Primeras Jornadas de Teoría de Números. Publ. Mat. (2007), 131--146.

        J. Guàrdia, Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves. Ann. Inst. Fourier. 57 (2007), no. 4, 1253--1283.

        R. Moreno, J.-M. Miret, A. Rio, Generalization of Vélu's formulae for isogenies between elliptic curves. Proceedings of the Primeras Jornadas de Teoría de Números. Publ. Mat. (2007), 147--163.

        2006

        P. Bayer, J. Guàrdia, Hyperbolic uniformization of the Fermat curves. Ramanujan Journal 12 (2006), no. 2, 207--223.

        N. Bruin, V. Flynn, J. Gonzalez and V. Rotger, On finiteness conjectures for modular quaternion algebras. Math. Proc. Camb. Philos. Soc 141 (2006), no. 3, 383--408.

        G. Cardona, Representations of G_k-groups and twists of the genus two curve y^2=x^5-x. J. Algebra 303 (2006), no. 2, 707--721.

        J. González, V. Rotger, Non-elliptic Shimura curves of genus one. J. Math. Soc. Japan 58 (2006), no. 4, 927--948.

        J. González, V. Rotger, On finiteness conjectures for endomorphism algebras of abelian surfaces. Math. Proc. Camb. Philos. Soc. 141 (2006), no. 3, 383--408.

        A. Rio, Dyadic exercises for octahedral extensions. II. J. Number Theory 118 (2006), no. 2, 172--188.

        2005

        M. Alsina, Binary quadratic forms and Eichler orders. J. Théor. Nombres Bordeaux 17 (2005) no. 1, pp. 13-23.

        M. Baker, E. González-Jiménez, J. González, B. Poonen, Finiteness results for modular curves of genus at least 2. Amer. J. Math. 127 (2005), no. 6, 1325-1387.

        P. Bayer, J. Guàrdia, On equations defining fake elliptic curves. J. Théor. Nombres Bordeaux 17 (2005), no. 1, pp. 57-67.

        G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over fields of even characteristic. Math. Zeit. 250 (2005), no. 1, 177-201.

        G. Cardona, J. Quer, Field of moduli and field of definition for curves of genus 2. In Computational aspects of algebraic curves (T. Shaska, ed.) pp. 71-83., Lecture Notes Series on Computing 13 (World Scientific).

        L. Dieulefait, V. Rotger, On abelian surfaces with potential quaternionic multiplication. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 4, 617--624.

        J. Fernández, J.-C. Lario, A. Rio, On twists of the modular curves X(p). Bull. London Math. Soc. 37 (2005), 342--350.

        E. Ghate, E. González-Jiménez, J. Quer, On the Brauer class of modular endomorphim algebras. Int. Math. Res. Not. 12 (2005), 701--723.

        J. González, J. Guàrdia, V. Rotger, Abelian Surfaces of GL_2-type as Jacobians of curves. Acta Arit. 116 (2005), 263--287.

        J. C. Lario, M. Masdeu, A note on dihedral polynomials of prime degree. Indian J. Pure and Appl. Math. 36 (2005), 300--305.

        J.M. Miret, R. Moreno, A. Rio, M. Valls, Determining the 2-Sylow subgroup of an elliptic curve over a finite field. Math. Comp. 74 (2005), no. 249, 411--427.

        V. Rotger, A. Skorobogatov, A. Yafaev, Failure of the Hasse principle on Atkin-Lehner quotients of Shimura curves. Moscow Math. J. 5 (2005), no. 2, pp. 159--172.

        M. Vela, Resolution of a family of embedding problems with cyclic kernel. Rev. Mat. Iberoamericana 21 (2005), no. 1, 111--132.

        2004

        M. Alsina, P. Bayer, Quaternion orders, quadratic forms, and Shimura curves. CRM Monograph Series, 22. American Mathematical Society, Providence, RI, 2004.

        G. Cardona, Q-curves and abelian varieties of GL2 type arising from dihedral genus 2 curves. Modular Curves and Abelian Varieties, 45-52, Progr. Math. 224, Birkhäuser, 2004.

        L. V. Dieulefait, V. Rotger, The arithmetic of QM-abelian surfaces through their Galois representations. J. Algebra 281 (2004), no. 1, 124--143.

        S. Galbraith, V. Rotger, Easy decision Diffie-Hellman groups. LMS J. Comput. Math. 7 (2004), 201--218.

        J. González, J.-C. Lario, J. Quer, Arithmetic of Q-curves. Modular Curves and Abelian Varieties, 125-139, Progr. Math. 224, Birkhäuser, 2004.

        J. González, V. Rotger, Equations of Shimura curves of genus 2. Int. Math. Res. Not. 14 (2004), 661-674.

        J. Guàrdia, Jacobi Thetanullwerte, periods of elliptic curves and minimal equations. Math. Res. Lett. 11 (2004), no. 1, 115--123.

        J. Guàrdia, E. Torres, M. Vela, Stable models of elliptic curves, ring class fields and complex multiplication. In Algorithmic Number Theory, Lecture Notes in Computer Science vol. 3076 (2004), 250--262.

        V. Rotger, Shimura curves embedded in Igusa's threefold. Modular Curves and Abelian Varieties, 263-276, Progr. Math. 224, Birkhäuser, 2004.

        V. Rotger, Modular Shimura varieties and forgetful maps. Trans. Amer. Math. Soc. 356 (2004), no. 4, 1535--1550

        V. Rotger, The field of moduli of the quaternionic multiplication on abelian varieties.. Intern. J. Math. Sc. 52 (2004), 2795--2808.

        2003

        G. Cardona, On the number of curves over a finite field. Finite Fields Appl. 9 (2003) no. 4, pp. 505-526.

        J. Fernández, On octahedral extensions of Q and quadratic Q-curves. J. Théor. Nombres Bordeaux 15 (2003) no. 1, pp. 125-131.

        E. González, J. González, Modular curves of genus 2. Math. Comp. 72 (2003) no. 241, pp. 397-418. http://front.math.ucdavis.edu/math.NT/0105232

        J. Guàrdia, A family of arithmetic surfaces of genus 3. Pacific J. Math. 212 (2003) no. 1, pp. 71-91

        J. Jiménez-Urroz, T. Yang, Heegner zeros of theta functions. Trans. Amer. Math. Soc. 355 (2003) no. 10, pp. 4137-4149.

        V. Rotger, Quaternions, polarizations and class numbers. J. Reine Angew. Math. 561 (2003), pp. 177-197

        2002

        G. Coogan, J. Jiménez-Urroz, Mordell-Weil ranks of quadratic twists of pairs of elliptic curves. J. Number Theory 96 (2002), no. 2, 388-399.

        J. Fernández, J.-C. Lario, A. Rio, Octahedral Galois extensions arising from Q-curves of degree 2. Canad. J. Math. 54 (2002) no. 6, 1202-1228.
        http://front.math.ucdavis.edu/ANT/0301/

        E. González, J. González, J. Guàrdia, Computations on modular jacobian surfaces. Lecture notes in Computer Science 2369 (2002), 189-197.

        J. Guàrdia, Jacobian nullwerte and algebraic equations. J. Algebra 253 (2002) no. 1, 112-132.

        J.-C. Lario, R. Schoof, Some computations with Hecke rings and deformation rings, With an appendix by Amod Agashe and William Stein. Experiment. Math. 11 (2002) no. 2, 303-311.

        V. Rotger, On the group of automorphisms of Shimura curves and applications. Compositio Math. 132 (2002) no. 2, 229-241.

        M. Vela, Central simple Z/nZ-graded algebras. Comm. Algebra 30 (2002) no. 4, 1995-2021.

        2001

        G. E. Andrews, J. Jiménez-Urroz, K. Ono, q-series identities and values of certain L-functions. Duke Math. J. 108 (2001) no. 3, pp. 395-419.

        J. González, Isogenies of polyquadratic Q-curves to their Galois conjugates. Arch. Math. (Basel) 77 (2001) no. 5, pp. 383-390.

        J. González, On the j-invariants of the quadratic Q-curves. J. London Math. Soc. (2) 63 (2001) no. 1, pp. 52-68.

        E. González, J. González, Curves of genus 2 parametrized from modular curves. Actas EACA 2001, pp. 190-195.

        J. González, J.-C. Lario, Q-curves and their Manin ideals. Amer. J. Math. 123 (2001) no. 3, pp. 475-503.

        J. Guàrdia, Arakelov computations in genus 3 curves. J. Théor. Nombres Bordeaux 13 (2001) no. 1, pp. 157-165.

        J. Guàrdia, Explicit geometry on a family of curves of genus 3. J. London Math. Soc. (2) 64 (2001) no. 2, pp. 299-310.

        J. Quer, Fields of definition of Q-curves. J. Théor. Nombres Bordeaux 13 (2001) no. 1, pp. 275-285.

        J. Quer, Embedding problems over abelian groups and an application to elliptic curves. J. Algebra 237 (2001) no. 1, 186-202.

        2000

        M. Alsina, Dominios fundamentales modulares. Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000), no. 3, 309-322.

        F. Aguiló, J. González, E. Simó, M. Zaragoza, Broadcasting in odd graphs. Ars Combin. 56 (2000), pp. 211--222.

        J. González, On the division polynomials of elliptic curves. Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000) no. 3, pp. 377-381.

        J. González, Q-curves associated with rational points of quotient curves of X0(N). Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000) no. 3, pp. 383-390.

        J. Guàrdia, A fundamental domain for the Fermat curves and their quotients. Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000) no. 3, pp. 391-396.

        J. Quer, Q-curves and abelian varieties of GL2-type. Proc. London Math. Soc. (3) 81 (2000) no. 2, pp. 285-317.

        M. Vela, J. Symbolic Comput. 30 (2000) no. 6, pp. 811--842.