Magdaléna Tinková

activity

20242026

collaborators

6 papers

math.NT2026

Additively indecomposable quadratic forms over biquadratic and simplest cubic fields

Simona FryÅ¡ovÃ¡, MagdalÃ©na TinkovÃ¡

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…

math.NT2025

Linear constellations in primes with arithmetic restrictions

Christopher Frei, Joachim KÃ¶nig, MagdalÃ©na TinkovÃ¡

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…

math.NT2025

Sums of two units in number fields

MagdalÃ©na TinkovÃ¡, Robin Visser, Pavlo Yatsyna

Let $K$ be a number field with ring of integers $O_{K}$ . Let $N_{K}$ be the set of positive integers $n$ such that there exist units $\varepsilon, Î´\in \mathcal{O}…

math.NT2025

Additively indecomposable quadratic forms over totally real number fields

MagdalÃ©na TinkovÃ¡, 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…

math.NT2025

Additive structure of non-monogenic simplest cubic fields

We consider Shanks' simplest cubic fields $K$ for which the index $[O_{K} : Z [I ¨ ]]$ of a root $I ¨ $ of the defining parametric polynomial is $3$ . For them, we study t…

math.NT2024

Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables

We study a new connection between multidimensional continued fractions, such as Jacobi--Perron algorithm, and additively indecomposable integers in totally real cubic number fields…