• Artículo
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      Markoff-Rosenberger triples in arithmetic progression 

      González Jiménez, Enrique; Tornero Sánchez, José María (Elsevier, 2013-06)
      We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff ...
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      On simultaneous arithmetic progressions on elliptic curves 

      García Selfa, Irene; Tornero Sánchez, José María (Taylor & Francis, 2006)
      In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We ...
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      On the computation of the Apéry set of numerical monoids and affine semigroups 

      Márquez Campos, Guadalupe; Ojeda, Ignacio; Tornero Sánchez, José María (Springer, 2014-10-01)
      A simple way of computing the Apéry set of a numerical semigroup (or monoid) with respect to a generator, using Groebner ...
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      On the singular braid monoid of an orientable surface 

      Díaz Cantos, Jerónimo; González-Meneses López, Juan; Tornero Sánchez, José María (American Mathematical Society, 2004)
      In this paper we show that the singular braid monoid of an orientable surface can be embedded in a group. The proof is purely topological, making no use of the monoid presentation.
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      On the ubiquity of trivial torsion on elliptic curves 

      González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 2010-08)
      The purpose of this paper is to give a down-to-earth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.
    • Trabajo Fin de Grado
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      Primalidad 

      Muñoz Ramírez, Paula (2023)
      The aim of this work is to present a deterministic method that establishes with absolute certainty whether a given number ...
    • Trabajo Fin de Grado
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      El problema diofántico de Frobenius 

      Chacón Gómez, Manuel Jesús (2016-12)
      In this work, we study the diophantine Frobenius problem. First, in Chapter 1, we briefly present what are numerical ...
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      Quantum álgorithms for the combinatorial invariants of numerical semigroups 

      Ossorio Castillo, Joaquín (2019)
      It was back in spring 2014 when the author of this doctoral dissertation was finishing its master thesis, whose main ...
    • Trabajo Fin de Máster
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      Representaciones de Galois asociadas a curvas elípticas 

      Pineda Martín, Miguel (2023)
      J.P Serre made, in his article ’Proprietes galoisiénnés des points d’ordre fini des courbes elliptiques’ published in ...
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      Searching for simultaneous arithmetic progressions on elliptic curves 

      García Selfa, Irene; Tornero Sánchez, José María (Australian Mathematical Society, 2005-06)
      We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
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      Some combinatorial remarks on normal flatness in analytic spaces 

      Soto Prieto, Manuel Jesús; Tornero Sánchez, José María (Mathematical Society of the Republic of China, 2014-06)
      In this article we present a combinatorial treatment of normal flatness in analytic spaces, using the idea of equimultiple ...
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      Some geometric aspects of Puiseux surfaces 

      Tornero Sánchez, José María (European Mathematical Society, 2003)
      The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that ...
    • Trabajo Fin de Grado
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      El teorema de Nagell-Lutz 

      Cano Wall, Pablo (2022-06-01)
      The goal of this memory is to prove the Nagell-Lutz theorem, an important theorem about the rational torsion of elliptic ...
    • Trabajo Fin de Máster
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      Teoría de la Complejidad en Computación Cuántica 

      Camacho Moro, Jesús (2020-06-01)
      During the rst half of the 20th century, the need of faster calculations brought the rst computers to our world. Those ...
    • Trabajo Fin de Máster
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      The Néron-Ogg-Shafarevich Criterion for elliptic curves 

      Navas Orozco, Jesús (2020-09-07)
      This text is the required master thesis that the author needs to present in order to obtain his Master’s degree in ...
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      Thue equations and torsion groups of elliptic curves 

      García Selfa, Irene; Tornero Sánchez, José María (Elsevier, 2009-02)
      A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.
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      Torsion of rational elliptic curves over cubic fields 

      González Jiménez, Enrique; Najman, Filip; Tornero Sánchez, José María (Rocky Mountain Mathematics Consortium, 2016)
      Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion ...
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      Torsion of rational elliptic curves over quadratic fields 

      González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 2014-09)
      Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a quadratic number field.
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      Torsion of rational elliptic curves over quadratic fields II 

      González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 2016-03)
      Let E be an elliptic curve defined over Q and let G=E(Q)_tors be the associated torsion group. In a previous paper, the ...