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

Gouadri Marwa


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 deg(β) = 2. We
establish a transcendence criterion depending on the continued β-fraction of one element
of Fq((x−1)).


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