Diophantine Approximation in Finite Characteristic

Dinesh S. Thakur

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 757-765 from Springer

Abstract: Abstract In contrast to Roth’s theorem that all algebraic irrational real numbers have approximation exponent two, the distribution of the exponents for the function field counterparts is not even conjecturally understood. We describe some recent progress made on this issue. An explicit continued fraction is not known even for a single non-quadratic algebraic real number. We provide many families of explicit continued fractions, equations and exponents for non-quadratic algebraic laurent series in finite characteristic, including non-Riccati examples with both bounded or unbounded sequences of partial quotients.

Keywords: Continue Fraction; Diophantine Approximation; Continue Fraction Expansion; Acta Arith; Unbounded Sequence (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_46

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DOI: 10.1007/978-3-642-18487-1_46

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