On metric diophantine approximation in the field of formal Laurent series

Michael Fuchs*

*Corresponding author for this work

研究成果: Article同行評審

22 引文 斯高帕斯(Scopus)

摘要

B. deMathan (1970, Bull. Soc. Math. France Supl. Mem. 21) proved that Khintchine's Theorem has an analogue in the field of formal Laurent series. First, we show that in case of only one inequality this result can also be obtained by continued fraction theory. Then, we are interested in the number of solutions and show under special assumptions that one gets a central limit theorem, a law of iterated logarithm and an asymptotic formula. This is an analogue of a result due to W. J. LeVeque (1958, Trans. Amer. Math. Soc. 87, 237-260). The proof is based on probabilistic results for formal Laurent series due to H. Niederreiter (1988, in Lecture Notes in Computer Science, Vol. 330, pp. 191-209, Springer-Verlag, New York/Berlin).

原文English
頁(從 - 到)343-368
頁數26
期刊Finite Fields and their Applications
8
發行號3
DOIs
出版狀態Published - 1 一月 2002

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