A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
Acta Arithmetica, Tome 61 (1992) no. 1, pp. 51-67
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_aa_61_1_51_67,
author = {Jun-ichi Tamura},
title = {A class of transcendental numbers with explicit g-adic expansion and the {Jacobi-Perron} algorithm},
journal = {Acta Arithmetica},
pages = {51--67},
year = {1992},
volume = {61},
number = {1},
doi = {10.4064/aa-61-1-51-67},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa-61-1-51-67/}
}
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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 61 (1992) no. 1, pp. 51-67. doi: 10.4064/aa-61-1-51-67
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