Now showing items 1-20 of 27

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      A complete diophantine characterization of the rational torsion of an elliptic curve  [Article]

      García Selfa, Irene; Tornero Sánchez, José María (Springer, 2012-01)
      We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non–)existence of integral solutions of a system of diophantine equations.
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      Algoritmos fundamentales en computación cuántica  [Master's Thesis]

      Pastor Díaz, Ulises (2019)
      At any point in history, we can find examples of problems solved mechanically, but it was in the 20th century with the arrival of computers that the paradigm shifted and the concept of problem-solving changed forever. It ...
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      Aspectos locales de singularidades de superficies superficies de Puiseux  [PhD Thesis]

      Tornero Sánchez, José María (2001)
      La memoria se articula en tres capítulos. En el primer capítulo se fijan definiciones y propiedades conocidas. Superficies algebroides, explosiones, divisor excepcional, cono tangente. Así mismo se prueban resultados ...
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      El ataque polaco al protocolo Enigma  [Final Degree Work]

      Gallardo Gómez, Rocío (2016)
      El principal objetivo de nuestro trabajo será desvelar las claves del exitoso ataque polaco al protocolo Enigma protagonizado por Marian Rejewski. Para ello, detallaremos el contexto histórico en el que se produjo dicho ...
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      Cálculo de invariantes combinatorios de semigrupos numéricos y aplicaciones  [PhD Thesis]

      Márquez Campos, Guadalupe (2014)
      En esta tesis trata básicamente, de en primer lugar establecer una relación entre bases de Groebner y semigrupos numéricos y en segundo lugar utilizar dicha relación para obtener diversas aplicaciones y resultados. La ...
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      Computing the rational torsion of an elliptic curve using Tate normal form  [Article]

      García Selfa, Irene; Olalla Acosta, Miguel Ángel; Tornero Sánchez, José María (Elsevier, 2002-09)
      It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 ≤ n ≤ 10, or n = 12) lie in a oneparameter family. However, this fact does not appear to have been used ever for ...
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      Códigos correctores de errores cuánticos  [Final Degree Work]

      Pastor Díaz, Ulises (2018)
      We could start our story talking about the revolution of quantum mechanics and the need to decipher the mystery that it creates, or we could start by talking about the birth of modern computation, which changed the world ...
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      Equimultiple locus of embedded algebroid surfaces and blowing-up in arbitrary characteristic  [Article]

      Piedra Sánchez, Ramón; Tornero Sánchez, José María (Chinese Academy of Sciences, 2009-12)
      This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing–up, to arbitrary characteristic.
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      Equimultiple locus of embedded algebroid surfaces and blowing-up in characteristic zero  [Article]

      Piedra Sánchez, Ramón; Tornero Sánchez, José María (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 2004)
      The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution process, both classical and modern.In this paper we explore how it changes by blowing–up.
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      Galois Theory, discriminants and torsion subgroups of elliptic curves  [Article]

      García Selfa, Irene; González Jiménez, Enrique; Tornero Sánchez, José María (Elsevier, 2010-08)
      We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the ...
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      Hironaka's characteristic polygon and effective resolution of surfaces  [Article]

      Piedra Sánchez, Ramón; Tornero Sánchez, José María (Elsevier, 2007-03-01)
      Hironaka’s concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool ...
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      Integral points in rational polygons: a numerical semigroup approach  [Article]

      Márquez Campos, Guadalupe; Ramírez Alfonsín, Jorge Luis; Tornero Sánchez, José María (Springer, 2016)
      In this paper we use an elementary approach by using numerical semigroups (specifically, those with two generators) to give a formula for the number of integral points inside a right-angled triangle with rational ...
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      Leyes de reciprocidad (cuatro demostraciones de la Ley de Reciprocidad Cuadrática)  [Final Degree Work]

      Sevillano Castellano, Eric (2018)
      A lo largo del siguiente trabajo vamos a profundizar en los contenidos impartidos en la asignatura Estructuras Algebraicas para explicar la Ley de Reciprocidad Cuadrática así como sus aplicaciones para la Teoría Algebraica ...
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      Markoff-Rosenberger triples in arithmetic progression  [Article]

      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 equation). We specifically focus on looking for solutions in arithmetic progression that lie in ...
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      On simultaneous arithmetic progressions on elliptic curves  [Article]

      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 first motivate this diophantine problem, prove some results, provide a number of interesting examples ...
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      On the singular braid monoid of an orientable surface  [Article]

      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  [Article]

      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.
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      El problema diofántico de Frobenius  [Final Degree Work]

      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 semigroups and we see what is the Frobenius number. By the end of this chapter we show that the Frobenius ...
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      Quantum álgorithms for the combinatorial invariants of numerical semigroups  [PhD Thesis]

      Ossorio Castillo, Joaquín (2019)
      It was back in spring 2014 when the author of this doctoral dissertation was finishing its master thesis, whose main objective was the understanding of Peter W. Shor’s most praised result, a quantum algorithm capable ...