Computation of L⊙ in the Tribonacci base

Abstract

The purpose of this paper is to study the quantities L_⊕ (resp. L_⊙) dened respectively as the maximal nite length of the -fractional part  appearing when one adds (resp. multiplies) two β-integers. We start by establishing some conditions for niteness of L_⊕ (resp.L_⊙). Then we determine the exact value of L_⊙ for the Tribonacci number.

Key words: Algebraic number, β-expansion, Tribonacci number.