Summary: [Page 1]
Cubic Pisot units with nite beta
expansions
Shigeki Akiyama
Abstract. Cubic Pisot units with nite beta expansion property are classied (Theorem
3). The results of [6] and [3] are well combined to complete its proof. Further, it is noted
that the above niteness property is equivalent to an important problem of fractal tiling
generated by Pisot numbers.
1991 Mathematics Subject Classication: 11K26,11A63,11Q15,28A80
1. Introduction and the results
Let  > 1 be a xed real number. Any positive real x is expanded as:
x =
1
X
i=N0
a i  i = a N0  N0 + a N0 1  N0 1 +



with a i 2 Z\ [0; ). Here we assume the 'greedy condition':
     x
N
X

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

Collections: Mathematics