Computation of L⊙(β) for some Pisot series in Fq((x−1))

Let β be a formal series over a finite field with deg⁡(β)=2. The aim of this paper is to give, for some Pisot series, the exact value of maximal length of the finite β-fractional parts in the β-expansion of product of two beta-polynomials (a formal series which has no β-fractional part), denoted L⊙(β).