Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11K60, 11J99, 11K38

Retrieve articles in all journals with MSC: 11K60, 11J99, 11K38


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290724-1
PII: S 0002-9947(1995)1290724-1
Keywords: Low-discrepancy sequences, $ (t,s)$-sequences, diophantine approximations of formal Laurent series
Article copyright: © Copyright 1995 American Mathematical Society