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Generalized $ (t,s)$-sequences, Kronecker-type sequences, and Diophantine approximations of formal Laurent series

Authors: Gerhard Larcher and Harald Niederreiter
Journal: Trans. Amer. Math. Soc. 347 (1995), 2051-2073
MSC: Primary 11K60; Secondary 11J99, 11K38
MathSciNet review: 1290724
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Abstract: The theory of $ (t,s)$-sequences leads to powerful constructions of low-discrepancy sequences in an $ s$-dimensional unit cube. We generalize this theory in order to cover arbitrary sequences constructed by the digital method and, in particular, the Kronecker-type sequences introduced by the second author. We define diophantine approximation constants for formal Laurent series over finite fields and show their connection with the distribution properties of Kronecker-type sequences. The main results include probabilistic theorems on the distribution of sequences constructed by the digital method and on the diophantine approximation character of $ s$-tuples of formal Laurent series over finite fields.

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Keywords: Low-discrepancy sequences, $ (t,s)$-sequences, diophantine approximations of formal Laurent series
Article copyright: © Copyright 1995 American Mathematical Society

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