紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2026, 63(1), p. 123-140

PERIODIC QUATERNION EXPANSION IN PISOT BASES

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

text

2026-01

In this paper, we consider a positional numeration system in ℝⁿ called the rotational beta expansion. The expansion of an element 𝓏 ∈ ℝⁿ is a sum of the form 𝓏 = (βM)⁻¹d₁ + (βM)⁻²d₂ + · · · , where the radix is βM for some fixed real number β > 1 and matrix M ∈ O(n). We reformulate the rotational beta expansion where M ∈ SO(4) into the so-called q-expansion on the set ℍ of real quaternions. In particular, we obtain necessary and sufficient conditions for the q-expansion of a quaternion to be periodic when the base q is a Pisot quaternion.

10.18910/103808

103808

PERIODIC QUATERNION EXPANSION IN PISOT BASES

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

2026-01

Osaka Journal of Mathematics

63

1

123

140

https://hdl.handle.net/11094/103808

10.18910/103808

https://doi.org/10.18910/103808