Výsledky vyhledávání - "J. L. Davison"

CONTINUED FRACTIONS WITH BOUNDED PARTIAL QUOTIENTS

Autor: J. L. Davison

Publikováno v: Proceedings of the Edinburgh Mathematical Society. 45:653-671

Precise bounds are given for the quantity$$ L(\alpha)=\frac{\limsup_{m\rightarrow\infty}(1/m)\ln q_m}{\liminf_{m\rightarrow\infty}(1/m)\ln q_m}, $$where $(q_m)$ is the classical sequence of denominators of convergents to the continued fraction $\alph

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ea4216dc784df69a478c110449afd91b
https://doi.org/10.1017/s001309150000119x

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Continued fractions for some alternating series

Autor: J. L. Davison, Jeffrey Shallit

Publikováno v: Monatshefte f�r Mathematik. 111:119-126

We discuss certain simple continued fractions that exhibit a type of “self-similar” structure: their partial quotients are formed by perturbing and shifting the denominators of their convergents. We prove that all such continued fractions represe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bcb0a71fde3e2bfbe7d3455755b58400
https://doi.org/10.1007/bf01332350

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Continued fractions and transcendental numbers

Autor: Boris Adamczewski, Yann Bugeaud, Les J. L. Davison

It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains arbitrarily

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5fdc61329e28c7b21e2de8ef32c7ca1
http://arxiv.org/abs/math/0511682

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A series and its associated continued fraction

Autor: J. L. Davison

Publikováno v: Proceedings of the American Mathematical Society. 63:29-32

Let α = ( 1 + √ 5 ) / 2 \alpha = (1 + \surd 5)/2 . In this paper it is proved that \[ [ u n k ] [unk] \] where t n = 2 f n − 2 {t_n} = {2^{{f_{n - 2}}}} and ( f n ) ({f_n}) is the Fibonacci sequence. It is also shown that T ( α ) T(\alpha ) is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::096d63066bd7dbbdd10e618688df4221
https://doi.org/10.1090/s0002-9939-1977-0429778-5

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A remarkable class of continued fractions

Autor: J. L. Davison, William W. Adams

Publikováno v: Proceedings of the American Mathematical Society. 65:194-198

For any irrational number α \alpha and integer a > 1 a > 1 , the continued fraction of ( a − 1 ) ∑ r = 1 ∞ 1 / a [ r α ] (a - 1)\sum _{r = 1}^\infty 1/{a^{[r\alpha ]}} is computed explicitly in terms of the continued fraction of α \alpha .

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::da4be7ad684b9c509e37c8e8e736772c
https://doi.org/10.1090/s0002-9939-1977-0441879-4

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Some Mappings Associated with the Permutation Groups

Autor: J. L. Davison

Publikováno v: Canadian Mathematical Bulletin. 20:71-75

Let Sn denote the permutation group on {1, 2, 3, …, n}. Let k ≥ 1 and n ≥ 1 be integers. For σ ∊ Sn we define ([1]) mk, n: Sn → Z byLet pn ∊ Sn be the reverse permutation: that is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9a6d344f01c1c48a00bf4245abbbf48f
https://doi.org/10.4153/cmb-1977-012-0

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A Result on Sums of Squares

Autor: J. L. Davison

Publikováno v: Canadian Mathematical Bulletin. 18:425-426

In this note we give an elementary proof of the following.Let be an integer. n≥1 Then, every positive even integer less than or equal to n(n2—1)/3 can be expressed as a sum ofn squares of integers from the set {0, 1, 2, …, n - 1}.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::018af4edde9d4647df46fee6c2c9f425
https://doi.org/10.4153/cmb-1975-078-1

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