Transcendental continued β-fraction with quadratic Pisot basis over fq((x−1))


Marwa Gouadri, Mohamed Hbaib




Let Fq be a finite field and Fq((x−1)) is the field of formal power series with coefficients in Fq. Let β ∈ Fq((x−1)) be a quadratic Pisot series with de1(β) = 2. We establish a transcendence criterion depending on the continued β-fraction of one element of Fq((x−1)),