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Uniform distribution of sequences in rings of integral matrices

Published online by Cambridge University Press:  18 May 2009

Harald Niederreiter  and
Jau-Shyong Shiue
Harald Niederreiter
Affiliation:
University of the West Indies, Kingston 7, Jamaica
Jau-Shyong Shiue
Affiliation:
National Chengchi University, Taipei, Taiwan University of South Florida, Tampa, Florida 33620, USA
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For various discrete commutative rings a concept of uniform distribution has already been introduced and studied, for example, for the ring of rational integers by Niven [9] (see also Kuipers and Niederreiter [2, Ch. 5]), for the rings of Gaussian and Eisenstein integers by Kuipers, Niederreiter, and Shiue [3], for rings of algebraic integers by Lo and Niederreiter [4], [7], and for finite fields by Gotusso [1] and Niederreiter and Shiue [8]. In the present paper, we shall show that a satisfactory theory of uniform distribution can also be developed in a noncommutative setting, namely for matrix rings over the rational integers.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 2 , July 1979 , pp. 169 - 178
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Gotusso, L., Successioni uniformemente distribuite in corpi finiti, Atti Sem. Mat. Fis. Univ. Modena 12 (1962/1963), 215–232.Google Scholar
2.Kuipers, L. and Niederreiter, H., Uniform Distribution of Sequences (Wiley-Interscience, 1974).Google Scholar
3.Kuipers, L., Niederreiter, H. and Shiue, J.-S., Uniform distribution of sequences in the ring of Gaussian integers, Bull. Inst. Math. Acad. Sinica 3 (1975), 311–325.Google Scholar
4.Lo, S. K. and Niederreiter, H., Banach-Buck measure, density, and uniform distribution in rings of algebraic integers, Pacific J. Math. 61 (1975), 191–208.CrossRefGoogle Scholar
5.Newman, M., Integral Matrices (Academic Press, 1972).Google Scholar
6.Niederreiter, H., On a class of sequences of lattice points, J. Number Theory 4 (1972), 477–502.CrossRefGoogle Scholar
7.Niederreiter, H. and Lo, S. K., Uniform distribution of sequences of algebraic integers, Math. J. Okayama Univ. 18 (1975), 13–29.Google Scholar
8.Niederreiter, H. and Shiue, J.-S., Equidistribution of linear recurring sequences in finite fields, Indagationes Math. 80 (1977), 397–405.CrossRefGoogle Scholar
9.Niven, I., Uniform distribution of sequences of integers, Trans. Amer. Math. Soc. 98 (1961), 52–61.CrossRefGoogle Scholar
10.Shiue, J.-S. and Hwang, C.-P., Complete residue systems in the ring of matrices of rational integers, Intemational J. of Math, and Math. Sci. 1 (1978), 217–225.CrossRefGoogle Scholar
11.Zame, A., On a problem of Narkiewicz concerning uniform distributions of sequences of integers, Colloq. Math. 24 (1972), 271–273.CrossRefGoogle Scholar