 
Summary: [Page 1]
Cubic Pisot units with finite beta
expansions
Shigeki Akiyama
Abstract. Cubic Pisot units with finite beta expansion property are classified (Theorem
3). The results of [6] and [3] are well combined to complete its proof. Further, it is noted
that the above finiteness property is equivalent to an important problem of fractal tiling
generated by Pisot numbers.
1991 Mathematics Subject Classification: 11K26,11A63,11Q15,28A80
1. Introduction and the results
Let > 1 be a fixed real number. Any positive real x is expanded as:
x =
i=N0
aii
= aN0 N0
+ aN01N01
+ · · ·
with ai Z [0, ). Here we assume the 'greedy condition':
x 
