A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
Jun-ichi Tamura
Acta Arithmetica, Tome 62 (1992), p. 51-67 / Harvested from The Polish Digital Mathematics Library
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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 t(φ,ψ) 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 ∈ ℤ). In the special case k = l = 1, our Theorems 1-3 have been shown in [15] by a different method using the theory of representation of numbers by Fibonacci numbers of third degree.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:206451 
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Jun-ichi Tamura. A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm. Acta Arithmetica, Tome 62 (1992) pp. 51-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav61i1p51bwm/

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