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pro vyhledávání: '"Hilgart, Tobias"'
Autor:
Hilgart, Tobias, Ziegler, Volker
We consider the simultaneous Pell equations $$x^2 - ay^2 = 1, \qquad z^2 - bx^2 = 1,$$ where $a > b\geq 2$ are positive integers. We describe a procedure which, for any fixed $b$, either confirms that the simultaneous Pell equations have at most one
Externí odkaz:
http://arxiv.org/abs/2406.06191
Autor:
Hilgart, Tobias
We consider a parametrised family of Thue equations, \[ (x-G_1(n)\, y) \cdots (x-G_d(n)\, y) - y^d = \pm 1, \] which was first considered by Thomas to have an explicit set of solutions for parameters $n$ larger than some effectively computable consta
Externí odkaz:
http://arxiv.org/abs/2406.01111
Autor:
Hilgart, Tobias, Ziegler, Volker
Related to Shank's notion of simplest cubic fields, the family of parametrised Diophantine equations, \[ x^3 - (n-1) x^2 y - (n+2) xy^2 - 1 = \left( x - \lambda_0 y\right) \left(x-\lambda_1 y\right) \left(x - \lambda_2 y\right) = \pm 1, \] was studie
Externí odkaz:
http://arxiv.org/abs/2404.18642
Autor:
Hilgart, Tobias, Ziegler, Volker
One of the first parametrised Thue equations, $$\left| X^3 - (n-1)X^2 Y - (n+2) XY^2 - Y^3 \right| = 1,$$ over the integers was solved by E. Thomas in 1990. If we interpret this as a norm-form equation, we can write this as $$\left| N_{K/\mathbb{Q}}\
Externí odkaz:
http://arxiv.org/abs/2306.11331
Autor:
Hilgart, Tobias, Ziegler, Volker
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent algebraic integers $\gamma_1, \dots, \gamma_s \in K^*$ that fulfil some technical requirements, which can be vastly simplified to $\mathbb{Q}$-linearly independenc
Externí odkaz:
http://arxiv.org/abs/2212.06405
Autor:
Hilgart, Tobias
Let $(A_n)_{n\in \mathbb{N}}, (B_n)_{n\in \mathbb{N}} \in \mathbb{Z}^{\mathbb{N}}$ be two linear-recurrent sequences that meet a dominant root condition and a few more technical requirements. We show that the split family of Thue equations \[ |X(X-A_
Externí odkaz:
http://arxiv.org/abs/2111.09568
Let $F_n$ denote the $n$-th Fibonacci number and $L_n$ the $n$-th Lucas number. We completely solve the family of cubic Thue equations $${(X-F_nY)(X-L_nY)X-Y^3=\pm1}$$ and show that there are no non-trivial solutions for $n\neq 1,3$.
Externí odkaz:
http://arxiv.org/abs/2106.03509
Autor:
Hilgart, Tobias
Publikováno v:
Publicationes Mathematicae Debrecen. 102:439-457
Let $(A_n)_{n\in \mathbb{N}}, (B_n)_{n\in \mathbb{N}} \in \mathbb{Z}^{\mathbb{N}}$ be two linear-recurrent sequences that meet a dominant root condition and a few more technical requirements. We show that the split family of Thue equations \[ |X(X-A_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9218e9d3cde2fc4c7288bc6888e48084
https://doi.org/10.5486/pmd.2023.9445
https://doi.org/10.5486/pmd.2023.9445
Autor:
Hilgart, Tobias
Tobias Hilgart Literaturverzeichnis: Blatt 40 Titel sollte lauten: "Grenzen klassischer Lerntheorie im Kontext neuronaler Netze" Paris-Lodron Universität Salzburg, Masterarbeit, 2021 (VLID)6439753
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______3941::f77587ee2f5e2ca68d3713a66c031876
Autor:
Hilgart, Tobias
Tobias Hilgart Literaturverzeichnis: Seite 72 Paris-Lodron Universität Salzburg, Masterarbeit, 2020 (VLID)6439749
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______3941::075efd7603afd47a96320ca0c19590f4