27 citations · 43 across the 4 of their papers we have counts for
5 papers · 1 filter
Trace and norm of indecomposable integers in cubic orders
Magdaléna Tinková
We study the structure of the codifferent and of additively indecomposable integers in families of totally real cubic fields. We prove that for cubic orders in these fields, the mi…
On the Pythagoras number of the simplest cubic fields
Magdaléna Tinková
The simplest cubic fields are generated by a root of the polynomial where . In this paper, we will show that the Pythagoras number…
Universal quadratic forms, small norms and traces in families of number fields
Vítězslav Kala, Magdaléna Tinková
We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of the simplest cubic fields and several other families of totally real number fields. As the…
Arithmetics in number systems with cubic base
Magdaléna Tinková
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional dig…
Universal Quadratic Forms and Indecomposables over Biquadratic Fields
Martin Čech, Dominik Lachman, Josef Svoboda +2
The aim of this article is to study (additively) indecomposable algebraic integers of biquadratic number fields and universal totally positive quadratic forms wi…