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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...
Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by $(ϕₘ)_{m∈ ℕ₀}$. The system $(ϕₘ)_{m∈ ℕ₀}$ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to $(ϕₘ)_{m∈ ℕ₀}$.This paper is a remark to Rutkowski's...
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