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A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm

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Tamura J.-i.

Acta Arithmetica

1992

tom 61

nr 1

51-67

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.

Hankel determinants for the Fibonacci word and Padé approximation

51%

Kamae T., Tamura J.-i., Wen Z.-Y.

Acta Arithmetica

1999

tom 89

nr 2

123-161

Ograniczanie wyników

2 Acta Arithmetica

2 Tamura J.-i.

1 Kamae T.

1 Wen Z.-Y.

1 1999

1 1992

Wyniki wyszukiwania

A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm

Hankel determinants for the Fibonacci word and Padé approximation