A Class of Periodic Jacobi-Perron Algorithms in Pure Algebraic Number Fields of Degree n...3.
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A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension
Jun-Ichi Tamura (1995)
Acta Arithmetica
A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
Jun-ichi Tamura (1992)
Acta Arithmetica
In this paper, we give transcendental numbers φ and ψ such that (i) both φ and ψ have explicit g-adic expansions, and simultaneously, (ii) the vector has an explicit expression in the Jacobi-Perron algorithm (cf. Theorem 1). Our results can be regarded as a higher-dimensional version of some of the results in [1]-[5] (see also [6]-[8], [10], [11]). The numbers φ and ψ have some connection with algebraic numbers with minimal polynomials x³ - kx² - lx - 1 satisfying (1.1) k ≥ l ≥0, k + l ≥ 2 (k,l...
A conjecture of Erdös on continued fractions
Walter Philipp (1976)
Acta Arithmetica
A Conjecture of Segre on Diophantine Approximation.
Jingcheng Tong (1991)
Monatshefte für Mathematik
A continued fraction proof of Ford's theorem on complex rational approximations.
Richard B. Lakein (1975)
Journal für die reine und angewandte Mathematik
A criterion for periodicity of multi-continued fraction expansion of multi-formal Laurent series
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
A dual approach to triangle sequences: a multidimensional continued fraction algorithm.
Assaf, Sami, Chen, Li-Chung, Cheslack-Postava, Tegan, Cooper, Benjamin, Diesl, Alexander, Garrity, Thomas, Lepinski, Mathew, Schuyle, Adam (2005)
Integers
A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities
Norman Richert (1990)
Acta Arithmetica
A generalization of Perron's theorem about Hurwitzian numbers
Pierre Stambul (1997)
Acta Arithmetica
A geometric method for the approximation by nearest integer continued fractions. (Eine geometrische Methode bei der Approximation durch Kettenbrüche nach dem nächsten Ganzen.)
Kopetzky, Hans Günther, Schnitzer, Franz Josef (1995)
Mathematica Pannonica
A growth bound on the partial quotients of cubic numbers.
J. Wolfskill (1984)
Journal für die reine und angewandte Mathematik
A localization theorem in the theory of diophantine approximation and an application to Pell's equation
A. Rockett, P. Szüsz (1986)
Acta Arithmetica
A new class of continued fraction expansions
Cor Kraaikamp (1991)
Acta Arithmetica
A proof of the continued fraction expansion of .
Komatsu, Takao (2007)
Integers
A remark on the theory of Diophantine approximations
Bohuslav Diviš, Břetislav Novák (1971)
Commentationes Mathematicae Universitatis Carolinae
A Result from Diophantine Approximation which has Applications in Economics.
H.C. Cheng, A.D. Pollington (1981)
Manuscripta mathematica
A Schinzel theorem on continued fractions in function fields
Weiqun Hu (2000)
Acta Arithmetica
A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields.
Arne J. Brentjes (1981)
Journal für die reine und angewandte Mathematik
A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties
Christian Drouin (2014)
Journal de Théorie des Nombres de Bordeaux
A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued...
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