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pro vyhledávání: '"11J70"'
Autor:
Langeveld, Niels, Ralston, David
Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their convergents and cla
Externí odkaz:
http://arxiv.org/abs/2412.05077
In this work, we develop two methods to obtain a factorisation as a product of bidiagonal matrices for the Hessenberg recurrence matrix of a system of multiple orthogonal polynomials. One method is based on the Gauss-Borel factorisation of the moment
Externí odkaz:
http://arxiv.org/abs/2412.03694
Autor:
Stange, Katherine E.
These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled "Number theor
Externí odkaz:
http://arxiv.org/abs/2412.02050
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