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Cubic Pisot units with finite beta Shigeki Akiyama
 

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
a-i-i
= a-N0 -N0
+ a-N0-1-N0-1
+
with ai Z [0, ). Here we assume the 'greedy condition':
x -

  

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

 

Collections: Mathematics