Results 11 to 20 of about 46,876 (239)
On the metric theory of
Indagationes Mathematicae, 2013 Let \(X=p\mathbb{Z}_p\) be the unit ball in the field of \(p\)-adic numbers \(\mathbb{Q}_p\), and define the map \(T:X\to X\) by \(T(x)=p^a/x-b\), where \(a=a(x)=v_p(x)\in\mathbb{N}\) is the \(p\)-adic valuation of \(x\), and \(b=b(x)\) is the unique element in \(\{1,\ldots,p-1\}\) such that \(p^a/x\equiv b \pmod{p\mathbb{Z}_p}\).
Hančl, J. +3 more
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A unifying theory for metrical results on regular continued fraction convergents and mediants [PDF]
, 2023 We revisit Ito's (\cite{I1989}) natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational.
K. Dajani, C. Kraaikamp, Slade Sanderson
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Metrical properties of exponentially growing partial quotients [PDF]
Forum mathematicum, 2023 A fundamental challenge within the metric theory of continued fractions involves quantifying sets of real numbers especially when their partial quotients exhibit specific growth rates.
Mumtaz Hussain, N. Shulga
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On the Metrical Theory of Continued Fractions [PDF]
Proceedings of the American Mathematical Society, 1994 Suppose b k {b_k} denotes either ϕ ( k ) \phi (k) or ϕ ( p k ) ( k = 1 , 2 , … ) \phi ({p_k})\;(k = 1 ...
openaire +1 more source
Continued fractions built from convex sets and convex functions [PDF]
, 2014 In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are provided.
Molchanov, Ilya
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, 2021 We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have Hausdorff dimension $
Stadlbauer, Manuel, Zhang, Xuan
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Partial sums of excursions along random geodesics and volume asymptotics for thin parts of moduli spaces of quadratic differentials [PDF]
, 2017 For a non-uniform lattice in SL(2, R), we consider excursions of a random geodesic in cusp neighborhoods of the quotient finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these excursions.
Gadre, Vaibhav
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On the metrical theory of a non-regular continued fraction expansion [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2015 Abstract We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the natural number with the unilateral shift.
Lascu Dan, Cîrlig George
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Geodesic Rosen Continued Fractions [PDF]
, 2015 We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's original work about words in Hecke groups, and it also helps us to identify ...
Short, Ian, Walker, Mairi
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, 2021 We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the digits of one
Lascu, Dan, Sebe, Gabriela Ileana
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