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of 749
pro vyhledávání: '"11J70"'
Autor:
Wu, Bingyao, Zhu, Jie-Xiang
Fix an irrational number $\alpha$. Let $X_1,X_2,\cdots$ be independent, identically distributed, integer-valued random variables with characteristic function $\varphi$, and let $S_n=\sum_{i=1}^n X_i$ be the partial sums. Consider the random walk $\{S
Externí odkaz:
http://arxiv.org/abs/2411.15724
Autor:
Yasutomi, Shin-ichi
J. Hurwitz introduced an algorithm that generates a continued fraction expansion for complex numbers $\alpha \in \mathbb{C}$, where the partial quotients belong to $(1+i)\mathbb{Z}[i]$. J. Hurwitz's work also provides a result analogous to Lagrange's
Externí odkaz:
http://arxiv.org/abs/2410.16683
Autor:
Karpenkov, Oleg, van Son, Matty
In this paper we develop a new geometric approach to subtractive continued fraction algorithms in high dimensions. We adapt a version of Farey summation to the geometric techniques proposed by F. Klein in 1895. More specifically we introduce Farey po
Externí odkaz:
http://arxiv.org/abs/2410.13091
Autor:
Romeo, Giuliano
Continued fractions have been generalized over the field of $p$-adic numbers, where it is still not known an analogue of the famous Lagrange's Theorem. In general, the periodicity of $p$-adic continued fractions is well studied and addressed as a har
Externí odkaz:
http://arxiv.org/abs/2410.09215
Autor:
Garrity, Thomas, Osterman, Otto Vaughn
We study the complexity of S-adic sequences corresponding to a family of 216 multi-dimensional continued fractions maps, called Triangle Partition maps (TRIP maps), with an emphasis on those with low upper bounds on complexity. Our main result is to
Externí odkaz:
http://arxiv.org/abs/2410.02032
Autor:
Lasjaunias, Alain
This note is a complement to an article which was published, six years ago, in The Ramanujan Journal (vol. 45.3, 2018). Here, the goal is to fully describe a singular transcendental continued fraction in Q((T^-1)), tied to a particular infinite two l
Externí odkaz:
http://arxiv.org/abs/2409.20233
The aim of this article is to study the regularity properties of the Wilton functions $W_\alpha$ associated with $\alpha$-continued fractions. We prove that the Wilton function is BMO for $\alpha\in[1-g,g]$ (where $g:=\frac{\sqrt{5}-1}{2}$ denotes th
Externí odkaz:
http://arxiv.org/abs/2409.20401
Autor:
Garrity, Thomas, Duke, Jacob Lehmann
Our goal is to show that both the fast and slow versions of the triangle map (a type of multi-dimensional continued fraction algorithm) in dimension $n$ are ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This particular type of
Externí odkaz:
http://arxiv.org/abs/2409.05822
We develop a versatile framework which allows us to rigorously estimate the Hausdorff dimension of maximal conformal graph directed Markov systems in $\mathbb{R}^n$ for $n \geq 2$. Our method is based on piecewise linear approximations of the eigenfu
Externí odkaz:
http://arxiv.org/abs/2408.06330
Autor:
Moshchevitin, Nikolay, Shulga, Nikita
For a norm $F$ on $\mathbb{R}^2$, we consider the set of $F$-Dirichlet improvable numbers $\mathbf{DI}_F$. In the most important case of $F$ being an $L_p$-norm with $p=\infty$, which is a supremum norm, it is well-known that $\mathbf{DI}_F = \mathbf
Externí odkaz:
http://arxiv.org/abs/2408.06200