On metric Diophantine approximation in positive characteristic
نویسندگان
چکیده
منابع مشابه
A Metric Theorem for Restricted Diophantine Approximation in Positive Characteristic
0 whenever ai = 0 for all i ∈ Z, k whenever an 6= 0 and ai = 0 for i < n. We can interpret F(X) as the completion of F(X) in this absolute value. Diophantine approximation in F(X), where a generic element is approximated by elements from the field of fractions F(X), has been studied by numerous authors (the survey papers [9, 11] contain some of the known results). Broadly speaking, the object o...
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We establish the conjectures of Sprindžhuk over a local field of positive characteristic. The method of KleinbockMargulis for the characteristic zero case is adapted.
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In a recent paper, Inoue and Nakada proved a 0-1 law and a strong law of large numbers with error term for the number of coprime solutions of the one-dimensional Diophantine approximation problem in the field of formal Laurent series over a finite base field. In this note, we generalize their results to higher dimensions.
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We consider inhomogeneous Diophantine approximation for formal Laurent series over a finite base field. We establish an analogue of a strong law of large numbers due to W. M. Schmidt with a better error term than in the real case. A special case of our result improves upon a recent result by H. Nakada and R. Natsui and completes a result of M. M. Dodson, S. Kristensen, and J. Levesley. Moreover...
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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 exp...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa110-3-1