BETA-EXPANSIONS WITH PISOT BASES OVER Fq((x-1))

It is well known that if the beta-expansion of any nonnegatiye integer is finite, then beta is a Pisot or Salem number. We prove here that in Fq((x(-1))), the beta-expansion of the polynomial part of beta is finite if and only if beta is a Pisot series. Consequently we give an other proof of Scheicher theorem about finiteness property in F-q((x(-1))). Finally we show that if the base beta is a Pisot series, then there is a bound of the length of the fractional part of beta-expansion of any polynomial P in F-q[x].