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Continued Fractions for Algebraic Formal Power Series over a Finite Base Field

✍ Scribed by Alain Lasjaunias

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 115 KB
Volume: 5
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1998.0236

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✦ Synopsis

We consider the continued fraction expansion of certain algebraic formal power series when the base field is finite. We are concerned with the property of the sequence of partial quotients being bounded or unbounded. We formalize the approach introduced by Baum and Sweet (1976), which applies to the elements of a particular subset of algebraic power series. We illustrate this method with a result when the base field is % .

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We will exhibit certain continued fraction expansions for power series over a "nite "eld, with all the partial quotients of degree one, which are non-quadratic algebraic elements over the "eld of rational functions.