Kronecker-type sequences and nonarchimedean diophantine approximations

Gerhard Larcher; Harald Niederreiter

Acta Arithmetica (1993)

  • Volume: 63, Issue: 4, page 379-396
  • ISSN: 0065-1036

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Gerhard Larcher, and Harald Niederreiter. "Kronecker-type sequences and nonarchimedean diophantine approximations." Acta Arithmetica 63.4 (1993): 379-396. <http://eudml.org/doc/206530>.

@article{GerhardLarcher1993,
author = {Gerhard Larcher, Harald Niederreiter},
journal = {Acta Arithmetica},
keywords = {-nets; -sequences; discrepancy; Kronecker-type sequences; nonarchimedean diophantine approximation; continued fractions},
language = {eng},
number = {4},
pages = {379-396},
title = {Kronecker-type sequences and nonarchimedean diophantine approximations},
url = {http://eudml.org/doc/206530},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Gerhard Larcher
AU - Harald Niederreiter
TI - Kronecker-type sequences and nonarchimedean diophantine approximations
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 4
SP - 379
EP - 396
LA - eng
KW - -nets; -sequences; discrepancy; Kronecker-type sequences; nonarchimedean diophantine approximation; continued fractions
UR - http://eudml.org/doc/206530
ER -

References

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  1. [1] J. V. Armitage, An analogue of a problem of Littlewood, Mathematika 16 (1969), 101-105. Zbl0188.35002
  2. [2] J. V. Armitage, Corrigendum and addendum: An analogue of a problem of Littlewood, Mathematika 17 (1970), 173-178. 
  3. [3] L. E. Baum and M. M. Sweet, Badly approximable power series in characteristic 2, Ann. of Math. 105 (1977), 573-580. Zbl0352.10017
  4. [4] H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351. Zbl0442.10035
  5. [5] T. Hansen, G. L. Mullen and H. Niederreiter, Good parameters for a class of node sets in quasi-Monte Carlo integration, Math. Comp., to appear. Zbl0792.11025
  6. [6] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974. Zbl0281.10001
  7. [7] G. Larcher, Über die isotrope Diskrepanz von Folgen, Arch. Math. (Basel) 46 (1986), 240-249. Zbl0568.10029
  8. [8] G. Larcher, On the distribution of s-dimensional Kronecker-sequences, Acta Arith. 51 (1988), 335-347. Zbl0611.10033
  9. [9] G. Larcher, On the distribution of the multiples of an s-tupel of real numbers, J. Number Theory 31 (1989), 367-372. Zbl0671.10047
  10. [10] G. Larcher, Nets obtained from rational functions over finite fields, this volume, 1-13. Zbl0770.11040
  11. [11] H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. Zbl0404.65003
  12. [12] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. Zbl0626.10045
  13. [13] H. Niederreiter, Quasi-Monte Carlo methods for multidimensional numerical integration, in: Numerical Integration III, H. Braß and G. Hämmerlin (eds.), Internat. Ser. Numer. Math. 85, Birkhäuser, Basel 1988, 157-171. Zbl0662.65021
  14. [14] H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70. Zbl0651.10034
  15. [15] H. Niederreiter, The probabilistic theory of linear complexity, in: Advances in Cryptology - EUROCRYPT'88, C. G. Günther (ed.), Lecture Notes in Comput. Sci. 330, Sprin- ger, Berlin 1988, 191-209. 
  16. [16] H. Niederreiter, Low-discrepancy point sets obtained by digital constructions over finite fields, Czechoslovak Math. J. 42 (1992), 143-166. Zbl0757.11024
  17. [17] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia 1992. Zbl0761.65002
  18. [18] H. Niederreiter, Finite fields, pseudorandom numbers, and quasirandom points, in: Proc. Internat. Conf. on Finite Fields (Las Vegas 1991), Dekker, New York 1992, 375-394. Zbl0792.11053
  19. [19] W. M. Schmidt, Irregularities of distribution, VII, Acta Arith. 21 (1972), 45-50. Zbl0244.10035
  20. [20] J. Schoißengeier, On the discrepancy of (nα), Acta Arith. 44 (1984), 241-279. 
  21. [21] I. M. Sobol', The distribution of points in a cube and the approximate evaluation of integrals, Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967), 784-802 (in Russian). 
  22. [22] Y. Taussat, Approximation diophantienne dans un corps de séries formelles, Thèse, Université de Bordeaux, 1986. 

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