Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T23:44:01.976Z Has data issue: false hasContentIssue false

Uniform distribution of sequences in rings of integral quaternions

Published online by Cambridge University Press:  18 May 2009

L. Kuipers
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
Jau-Shyong Shiue
Affiliation:
Department of Mathematical Sciences, National Chengchi University, Taipei, TaiwanR.O.C.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ℤ and ℤ[i] have their usual meaning. Let Yo denote the noncommutative ring of integral quaternions, that is the set of all elements a + bi + cj + dk with a, b, c, d ∈ ℤ and where i, j and k together with the number 1 are the four units of the system of quaternions.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Kuipers, L. and Niederreiter, H., Uniform distribution of sequences (Wiley-Interscience, New York, 1974).Google Scholar
2.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), 311325.Google Scholar
3.Niederreiter, H., On a class of sequences of lattice points, J. Number Theory 4 (1972), 477502.CrossRefGoogle Scholar
4.Niven, I., Uniform distribution of sequences of integers, Trans. Amer. Math. Soc. 98 (1961), 5261.CrossRefGoogle Scholar
5.Shiue, J.-S. and Hwang, C.-P., A note on a complete residue system in the ring of integral quaternions, Soochow J. Math. Natur. Sci. 5 (1979), 193196.Google Scholar
6.Zame, A., On a problem of Narkiewicz concerning uniform distributions of sequences of integers, Colloq. Math. 24 (1972), 271273.CrossRefGoogle Scholar