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Diophantine Approximation Exponents and Continued Fractions for Algebraic Power Series

✍ Scribed by Dinesh S. Thakur

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 100 KB
Volume: 79
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2413

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✦ Synopsis

For each rational number not less than 2, we provide an explicit family of continued fractions of algebraic power series in finite characteristic (together with the algebraic equations they satisfy) which has that rational number as its diophantine approximation exponent. We also provide some non-quadratic examples with bounded sequences of partial quotients.

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✍ Alain Lasjaunias 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 115 KB

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