SciELO - Scientific Electronic Library Online

SciELO - Scientific Electronic Library Online

Referencias del artículo

SHPARLINSKI, Igor E.. Exponents of Modular Reductions of Families of Elliptic Curves. Rev. Unión Mat. Argent. [online]. 2009, vol.50, n.1, pp. 69-74. ISSN 0041-6932.

    [1]    W. D. Banks and I. E. Shparlinski, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel J. Math., (to appear). [ Links ]

    [2]    A. Cojocaru and C. Hall, 'Uniform results for Serre's theorem for elliptic curves', Internat. Math. Res. Notices, 2005 (2005), 3065-3080. [ Links ]

    [3]    A. Cojocaru and I. E. Shparlinski, 'Distribution of Farey fractions in residue classes and Lang-Trotter conjectures on average', Proc. Amer. Math. Soc., 136 (2008), 1977-1986. [ Links ]

    [4]    W. Duke, 'Almost all reductions modulo p of an elliptic curve have a large exponent', Comptes Rendus Mathematique, 337 (2003), 689-692. [ Links ]

    [5]    K. Ford and I. E. Shparlinski, 'On finite fields with Jacobians of small exponent', Preprint, 2006 (available from [ Links ]

    [6]    H. Iwaniec and E. Kowalski, On curves over finite fields with Jacobians of small exponent. Intern. J. Number Theory, 4, 2008, 819-826. [ Links ]

    [7]    F. Luca, J. McKee and I. E. Shparlinski, 'Small exponent point groups on elliptic curves', J. Théorie des Nombres Bordeaux, 18 (2006), 471-476. [ Links ]

    [8]    F. Luca and I. E. Shparlinski, 'On the exponent of the group of points on elliptic curves in extension fields', Intern. Math. Research Notices, 2005 (2005), 1391-1409. [ Links ]

    [9]    R. Schoof, 'The exponents of the group of points on the reduction of an elliptic curve', Arithmetic Algebraic Geometry, Progr. Math., vol. 89, Birkhäuser, Boston, MA, 1991, 325-335. [ Links ]

    [10]    I. E. Shparlinski, 'Orders of points on elliptic curves', Affine Algebraic Geometry, Contemp. Math., vol. 369, Amer. Math. Soc., Providence, RI, 2005, 245-252. [ Links ]

    [11]    J. H. Silverman, The arithmetic of elliptic curves, Springer-Verlag, Berlin, 1995. [ Links ]