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Papers by Paraskevas Alvanos

Research paper thumbnail of Bounds for the smallest integral solutionof Pell equation over a number field

Functiones et Approximatio Commentarii Mathematici

Research paper thumbnail of Integer Solutions of the Equation y2 = Ax4 + B

Journal of Integer Sequences, 2015

Let A ∈ {k 2 (k 2 l 2 + 1), 4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers, and ... more Let A ∈ {k 2 (k 2 l 2 + 1), 4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers, and let B be a non-zero square-free integer such that |B| < √ A. In this paper we determine all the possible integer solutions of the equation y 2 = Ax 4 + B by using terms of Lucas sequences of the form mx 2 .

Research paper thumbnail of 8 Computing Integral Points on Rational Curves

Riemann-Roch Spaces and Computation

Research paper thumbnail of 7 Computing Resultant and Norm Form Equations

Riemann-Roch Spaces and Computation

Research paper thumbnail of 2 Function Fields and Curves

Riemann-Roch Spaces and Computation

Research paper thumbnail of Index of Algorithms

Riemann-Roch Spaces and Computation

Research paper thumbnail of 5 Computing Integral Bases

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of 4 Integral Domains

Riemann-Roch Spaces and Computation

Research paper thumbnail of 1 Elements of Algebra

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of 3 Riemann-Roch Spaces

Riemann-Roch Spaces and Computation

Research paper thumbnail of Characterizing Algebraic Curves with Infinitely Many Integral Points

International Journal of Number Theory, 2009

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curveC ov... more A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curveC over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper, we give necessary and sufficient conditions for C to have infinitely many S-integral points.

Research paper thumbnail of Solving genus zero Diophantine equations over number fields

Journal of Symbolic Computation, 2011

Research paper thumbnail of Characterizing algebraic curves with

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C o... more A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper we give necessary and sufficient conditions for C to have infinitely many S-integral points.

Research paper thumbnail of Integer Solutions of the Equation y2 = Ax4 + B

J. Integer Seq., 2015

Let A ∈ {k 2 (k 2 l 2 + 1),4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers,

Research paper thumbnail of Riemann-Roch Spaces and Computation

The book is focused on Riemann-Roch spaces and on the computation of algebraic structures connect... more The book is focused on Riemann-Roch spaces and on the computation of algebraic structures connected to the Riemann-Roch theorem.

Research paper thumbnail of 6 Computing Riemann-Roch Spaces

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of Literal shuffle product of fuzzy musical languages

Research paper thumbnail of Bounds for the smallest integral point on a conic over a number field

Research paper thumbnail of Solving Norm Form Equations over Number Fields

Lecture Notes in Computer Science, 2009

ABSTRACT Let K be a number field and L a finite extension of K of degree ℓ. Let ω 1 = 1,ω 2,..., ... more ABSTRACT Let K be a number field and L a finite extension of K of degree ℓ. Let ω 1 = 1,ω 2,..., ω ℓ be K-linearly independent integers of L and k an integer of K. We denote by N L/K the norm from L to K. In this paper we give an algorithm for the computation of algebraic integers, x 1,..., x ℓ ∈ K satisfying the equation N L/K (ω 1 x 1 + ⋯ + x ℓ ω ℓ) = k.

Research paper thumbnail of Bounds for the smallest integral solutionof Pell equation over a number field

Functiones et Approximatio Commentarii Mathematici

Research paper thumbnail of Integer Solutions of the Equation y2 = Ax4 + B

Journal of Integer Sequences, 2015

Let A ∈ {k 2 (k 2 l 2 + 1), 4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers, and ... more Let A ∈ {k 2 (k 2 l 2 + 1), 4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers, and let B be a non-zero square-free integer such that |B| < √ A. In this paper we determine all the possible integer solutions of the equation y 2 = Ax 4 + B by using terms of Lucas sequences of the form mx 2 .

Research paper thumbnail of 8 Computing Integral Points on Rational Curves

Riemann-Roch Spaces and Computation

Research paper thumbnail of 7 Computing Resultant and Norm Form Equations

Riemann-Roch Spaces and Computation

Research paper thumbnail of 2 Function Fields and Curves

Riemann-Roch Spaces and Computation

Research paper thumbnail of Index of Algorithms

Riemann-Roch Spaces and Computation

Research paper thumbnail of 5 Computing Integral Bases

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of 4 Integral Domains

Riemann-Roch Spaces and Computation

Research paper thumbnail of 1 Elements of Algebra

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of 3 Riemann-Roch Spaces

Riemann-Roch Spaces and Computation

Research paper thumbnail of Characterizing Algebraic Curves with Infinitely Many Integral Points

International Journal of Number Theory, 2009

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curveC ov... more A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curveC over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper, we give necessary and sufficient conditions for C to have infinitely many S-integral points.

Research paper thumbnail of Solving genus zero Diophantine equations over number fields

Journal of Symbolic Computation, 2011

Research paper thumbnail of Characterizing algebraic curves with

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C o... more A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper we give necessary and sufficient conditions for C to have infinitely many S-integral points.

Research paper thumbnail of Integer Solutions of the Equation y2 = Ax4 + B

J. Integer Seq., 2015

Let A ∈ {k 2 (k 2 l 2 + 1),4k 2 (k 2 (2l − 1) 2 + 1)}, where k and l are positive integers,

Research paper thumbnail of Riemann-Roch Spaces and Computation

The book is focused on Riemann-Roch spaces and on the computation of algebraic structures connect... more The book is focused on Riemann-Roch spaces and on the computation of algebraic structures connected to the Riemann-Roch theorem.

Research paper thumbnail of 6 Computing Riemann-Roch Spaces

Riemann-Roch Spaces and Computation, 2015

Research paper thumbnail of Literal shuffle product of fuzzy musical languages

Research paper thumbnail of Bounds for the smallest integral point on a conic over a number field

Research paper thumbnail of Solving Norm Form Equations over Number Fields

Lecture Notes in Computer Science, 2009

ABSTRACT Let K be a number field and L a finite extension of K of degree ℓ. Let ω 1 = 1,ω 2,..., ... more ABSTRACT Let K be a number field and L a finite extension of K of degree ℓ. Let ω 1 = 1,ω 2,..., ω ℓ be K-linearly independent integers of L and k an integer of K. We denote by N L/K the norm from L to K. In this paper we give an algorithm for the computation of algebraic integers, x 1,..., x ℓ ∈ K satisfying the equation N L/K (ω 1 x 1 + ⋯ + x ℓ ω ℓ) = k.

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