Summary: PISOT NUMBERS AND GREEDY ALGORITHM
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.
Let be the fixed real number greater than 1 and x be a positive real number.
Then the expansion of the form x =
is said to be a greedy expansion
(G) |x -
| < -N
holds for every N and ai is a non negative integer with 0 ai < . It is a natural