1 citations · 2 across the 7 of their papers we have counts for
7 papers · 1 filter
Additively indecomposable quadratic forms over biquadratic and simplest cubic fields
Simona Fryšová, Magdaléna Tinková
In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find…
Additively indecomposable quadratic forms over totally real number fields
Magdaléna Tinková, Pavlo Yatsyna
We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real num…
Sums of two units in number fields
Magdaléna Tinková, Robin Visser, Pavlo Yatsyna
Let be a number field with ring of integers . Let be the set of positive integers such that there exist units $\varepsilon, δ\in \mathcal{O}_…
Linear constellations in primes with arithmetic restrictions
Christopher Frei, Joachim König, Magdaléna Tinková
We prove analogues of the theorem of Green and Tao on linear constellations in primes, in which the primes under consideration are restricted by certain arithmetic conditions. Our…
Bounds on the Pythagoras number and indecomposables in biquadratic fields
Magdaléna Tinková
We show that for all real biquadratic fields not containing , , , , and , the Pythagoras number of the ring of algebr…
Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables
Vítězslav Kala, Ester Sgallová, Magdaléna Tinková
We study a new connection between multidimensional continued fractions, such as Jacobi--Perron algorithm, and additively indecomposable integers in totally real cubic number fields…
Additive structure of non-monogenic simplest cubic fields
Daniel Gil-Muñoz, Magdaléna Tinková
We consider Shanks' simplest cubic fields for which the index of a root of the defining parametric polynomial is . For them, we study the…