Zobrazeno 1 - 10
of 5 877
pro vyhledávání: '"Algebraic integer"'
Let $d>k$ be positive integers. Motivated by an earlier result of Bugeaud and Nguyen, we let $E_{k,d}$ be the set of $(c_1,\ldots,c_k)\in\mathbb{R}_{\geq 0}^k$ such that $\vert\alpha_0\vert\vert\alpha_1\vert^{c_1}\cdots\vert\alpha_k\vert^{c_k}\geq 1$
Externí odkaz:
http://arxiv.org/abs/2408.00250
Autor:
Zhao, Jiuzhou, Li, Ruofan
Let $\alpha, \beta$ be two relatively prime algebraic integers in a number field $K$ and $N$ be a positive integer. We show that the number of $n\in\{1,2,\dots,N\}$ such that the $\beta$-adic expansion of $\alpha^n$ omits a given digit is less than $
Externí odkaz:
http://arxiv.org/abs/2405.06220
Autor:
Krachun, D., Petrov, F.
We prove an asymptotically tight lower bound on $|A+\lambda A|$ for $A\subset \mathbb{C}$ and algebraic integer $\lambda$. The proof combines strong version of Freiman's theorem, structural theorem on dense subsets of a hypercubic lattice and a gener
Externí odkaz:
http://arxiv.org/abs/2311.09399
Autor:
STANKOV, Dragan
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2019 Jan 01. 31(1), 215-226.
Externí odkaz:
https://www.jstor.org/stable/26730894
Autor:
Jang, Wonyong, Kim, KyeongRo
Let $\alpha \in \mathbb{R}$ and let $$A=\begin{bmatrix} 1 & 1 \\ 0 & 1\end{bmatrix} \ \text{and} \ B_{\alpha} = \begin{bmatrix} 1 & 0 \\ \alpha & 1\end{bmatrix}.$$ The subgroup $G_\alpha$ of $\mathrm{SL}_2(\mathbb{R})$ is a group generated by the mat
Externí odkaz:
http://arxiv.org/abs/2010.09560
Autor:
Rhin, Georges, Wu, Qiang
Publikováno v:
Mathematics of Computation, 2007 Apr 01. 76(258), 1025-1038.
Externí odkaz:
https://www.jstor.org/stable/40234415
Autor:
Seppälä, Louna
We study a linear form in the values of Euler's series $F(t)=\sum_{n=0}^\infty n!t^n$ at algebraic integer points $\alpha_1, \ldots, \alpha_m \in \mathbb{Z}_{\mathbb{K}}$ belonging to a number field $\mathbb{K}$. Let $v|p$ be a non-Archimedean valuat
Externí odkaz:
http://arxiv.org/abs/1809.10997
Autor:
Stankov, Dragan
Let $\alpha$ be an algebraic integer of degree $d$, which is reciprocal. The house of $\alpha$ is the largest modulus of its conjugates. We compute the minimum of the houses of all reciprocal algebraic integers of degree $d$ which are not roots of un
Externí odkaz:
http://arxiv.org/abs/1806.06424