Transcendental Continued β-Fraction with Formal Power Series over Finite Fields
Keywords:
Laurent series, finite fields, continued β-fractionAbstract
In the framework of formal power series defined over a finite field, this study provides a new theoretical result that facilitates the derivation of a transcendence criterion. Our approach specifically leverages the structural properties of continued β-fraction expansions associated with quadratic Pisot series, where deg(β) = m. By analysing these expansions, we establish conditions under which an element of Fq((x^(−1)) is transcendental.
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Copyright (c) 2026 Rania Kammoun
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