 
Summary: PISOT NUMBERS AND GREEDY ALGORITHM
Shigeki Akiyama
Niigata University
Abstract. We study the greedy expansion of real numbers in Pisot number base.
We will show a certain criterions of finiteness, periodicity, and purely periodicity.
Further, it is proved that every sufficiently small positive rational numbers has purely
periodic greedy expansion in Pisot unit base under a certain finiteness condition.
1. Introduction
Let be the fixed real number greater than 1 and x be a positive real number.
Then the expansion of the form x =
N0i aii
is said to be a greedy expansion
if
(G) x 
N0iN
aii
 < N
,
holds for every N and ai is a non negative integer with 0 ai < . It is a natural
