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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Generalized $(t,s)$-sequences, Kronecker-type sequences, and Diophantine approximations of formal Laurent series
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by Gerhard Larcher and Harald Niederreiter PDF
Trans. Amer. Math. Soc. 347 (1995), 2051-2073 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2051-2073
  • MSC: Primary 11K60; Secondary 11J99, 11K38
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1290724-1
  • MathSciNet review: 1290724