László Remete

activity

20182021

most citedPower integral bases in cubic and quartic extensions of real quadratic fields

4 citations · 4 across the 2 of their papers we have counts for

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Showing 2018Show all

11 papers · 1 filter

math.NT2018

Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields

István Gaál, Borka Jadrijević, László Remete

The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known. The family of simplest cubic Thue equations was already s…

math.NT2018

Totally real Thue inequalities over imaginary quadratic fields

István Gaál, Borka Jadrijević, László Remete

Let $F (x, y)$ be an irreducible binary form of degree $\geq 3$ with integer coefficients and with real roots. Let $M$ be an imaginary quadratic field, with ring of integers $Z_{M}$ . L…

math.NT2018

Calculating power integral bases by solving relative Thue equations

István Gaál, László Remete, Tí mea Szabó

In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type $1 0^{500}$ for the sizes of…

math.NT2018

Solving binomial Thue equations

István Gaál, László Remete

We consider binomial Thue equations of type $x^{n} - m y^{n} = \pm 1$ in $x, y \in Z$ . Optimizing the method of Peth\H o we perform an extensive calculation by a high performance computer to…

math.NT2018

Binomial Thue equations and power integral bases in pure quartic fields

István Gaál, László Remete

It is a classical problem in algebraic number theory to decide if a number field admits power integral bases and further to calculate all generators of power integral bases. This p…

math.NT2018

Non-monogenity in a family of octic fields

István Gaál, László Remete

Let $m$ be a square-free positive integer, $m \equiv 2, 3 (mod 4)$ . We show that the number field $K = Q (i, 4 m)$ is non-monogene, that is it does not admit any power in…