Geodesic
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.

Voir la notice de l'article provenant de 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.
DOI : 10.4064/aa-61-1-51-67

Jun-ichi Tamura 1

1 
@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},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1992},
     doi = {10.4064/aa-61-1-51-67},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa-61-1-51-67/}
}
TY  - JOUR
AU  - Jun-ichi Tamura
TI  - A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
JO  - Acta Arithmetica
PY  - 1992
SP  - 51
EP  - 67
VL  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa-61-1-51-67/
DO  - 10.4064/aa-61-1-51-67
LA  - en
ID  - 10_4064_aa_61_1_51_67
ER  - 
%0 Journal Article
%A Jun-ichi Tamura
%T A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
%J Acta Arithmetica
%D 1992
%P 51-67
%V 61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa-61-1-51-67/
%R 10.4064/aa-61-1-51-67
%G en
%F 10_4064_aa_61_1_51_67
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. http://geodesic.mathdoc.fr/articles/10.4064/aa-61-1-51-67/

Cité par Sources :