En 1915, Albert Einstein publica la teoría de la relatividad general convirtiéndose en la teoría de la gravedad con mayor ...

In this paper, we present a generalisation of the Phase Kick-Back technique, which is central to some of the classical ...

Universal quantum gates play a crucial role in quantum computing as they form the building blocks for quantum circuits. ...

J.P Serre made, in his article ’Proprietes galoisiénnés des points d’ordre fini des courbes elliptiques’ published in 1972 ...

The aim of this work is to present a deterministic method that establishes with absolute certainty whether a given number ...

The main purpose of this project is to develop the necessary theory to understand the Birch and Swinnerton-Dyer conjecture. ...

El objetivo de este trabajo es servirnos de las herramientas impartidas en la asignatura de Álgebra Conmutativa y Geometría ...

The goal of this memory is to prove the Nagell-Lutz theorem, an important theorem about the rational torsion of elliptic ...

This text is the required master thesis that the author needs to present in order to obtain his Master’s degree in ...

During the rst half of the 20th century, the need of faster calculations brought the rst computers to our world. Those ...

This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems ...

At any point in history, we can find examples of problems solved mechanically, but it was in the 20th century with the ...

It was back in spring 2014 when the author of this doctoral dissertation was finishing its master thesis, whose main ...

A lo largo del siguiente trabajo vamos a profundizar en los contenidos impartidos en la asignatura Estructuras Algebraicas ...

We could start our story talking about the revolution of quantum mechanics and the need to decipher the mystery that it ...

In this work, we study the diophantine Frobenius problem. First, in Chapter 1, we briefly present what are numerical ...

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 ...

El principal objetivo de nuestro trabajo será desvelar las claves del exitoso ataque polaco al protocolo Enigma protagonizado ...

In this paper we use an elementary approach by using numerical semigroups (specifically, those with two generators) to ...

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion ...

A simple way of computing the Apéry set of a numerical semigroup (or monoid) with respect to a generator, using Groebner ...

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.

In this article we present a combinatorial treatment of normal flatness in analytic spaces, using the idea of equimultiple ...

En esta tesis trata básicamente, de en primer lugar establecer una relación entre bases de Groebner y semigrupos numéricos ...

We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff ...

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.

We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to ...

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.

This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing–up, to arbitrary characteristic.

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.

Hironaka’s concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of ...

In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We ...

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.

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.

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.

The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that ...

It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 ≤ n ≤ 10, ...

La memoria se articula en tres capítulos. En el primer capítulo se fijan definiciones y propiedades conocidas. Superficies ...