Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-29T23:25:26.508Z Has data issue: false hasContentIssue false
  • English
  • Français

A diophantine problem on groups. III

Published online by Cambridge University Press:  24 October 2008

R. C. Baker
R. C. Baker
Affiliation:
Birkbeck College, University of London
Get access Rights & Permissions [Opens in a new window]

Abstract

The following generalization of a theorem of Weyl appeared in part I of this series of papers. Let G be a locally compact Abelian group with dual group ĝ. Let be a sequence in ĝ, not too slowly growing in a certain precise sense. Then, provided ĝ has ‘not too many’ elements of finite order, the sequences

are uniformly distributed on the circle, for almost all x in G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 31 - 47
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baker, R. C. A Diophantine problem on groups, I. To appear. Trans. Amer. Math. Soc.Google Scholar
(2)Baker, R. C. A Diophantme problem on groups, II. To appear. Proc. Lond. Math. Soc.Google Scholar
(3)Erdös, P. and Koksma, J. F.On the uniform distribution of sequences (f(n, θ)). Proc. Kon.. Ned. Akad. van Wetensch. 52 (1949), 851–854.Google Scholar
(4)Gál, I. S. and Koksma, J. F.Sur l'ordre do grandeur des fonctions sommables. C.R. Acad. Sci. (Paris) 227 (1948), 1321–1323.Google Scholar
(5)Hewitt, E. and Zuckerman, H. S.Continuous measures with absolutely continuous convolution squares. Proc. Camb. Phil. Soc. 62 (1966), 339–420.CrossRefGoogle Scholar
Corrigendum, Proc. Camb. Phil. Soc. 63 (1967), 367–368.CrossRefGoogle Scholar
(6)Hewitt, E. and Ross, K. A.Abstract harmonic analys8is I (Springer-Verlag, 1963).Google Scholar
(7)Kahane, J. P.Sur les mauvaises repartitions modulo 1. Ann. Inst. Fourier (Grenoble), 14 (1965), 519–526.CrossRefGoogle Scholar
(8)Kahane, J. P. and Salem, R.Distribution modulo one and sets of uniqueness. Bull. Amer. Math. Soc. 70 (1964), 259–261.CrossRefGoogle Scholar
(9)Rudin, W.Fourier analysis on groups. (Interscience, 1962.)Google Scholar
(10)Salem, R.Uniform distribution and capacity of sets. Communications Sem. Math. Univ. Lund. Supplement, 1952, pp. 193–195.Google Scholar
(11)Wiener, N. and Wintner, A.Fourier–Stieltjes transforms and singular infinite convolution. Amer. J. Math. 60 (1938), 513–522.CrossRefGoogle Scholar
(12)Zygmitnd, A.Trigonometric series. Second edition (Cambridge, 1959).Google Scholar