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Displaying similar documents to “Recurrences and Legendre transform.”

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

Jun-ichi Tamura (1992)

Acta Arithmetica

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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...