Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T13:57:56.363Z Has data issue: false hasContentIssue false
  • English
  • Français

On the fractional parts of certain additive forms

Published online by Cambridge University Press:  24 October 2008

R. C. Baker  and
J. Gajraj
R. C. Baker
Affiliation:
Royal Holloway CollegeEgham, Surrey
J. Gajraj
Affiliation:
Royal Holloway CollegeEgham, Surrey
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, k is a positive integer, k ≧ 2; K denotes 2k−1, and ε is an arbitrary positive number. X = (x1, …, xs) and U = (u1, …, ur) are integer vectors; is the distance from the real number y to the nearest integer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 3 , May 1976 , pp. 463 - 467
Copyright
Copyright © Cambridge Philosophical Society 1976

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)Cassels, J. W. S.An introduction to diophantine approximation (Cambridge University Press 1965).Google Scholar
(2)Cook, R. J.The fractional parts of an additive form. Proc. Cambridge Philos. Soc. 72 (1972), 209–212.CrossRefGoogle Scholar
(3)Danicic, I. Ph.D. thesis (London, 1957).Google Scholar
(4)Davenport, H.Analytic methods for diophantine equations and diophantine inequalities (Ann Arbor, Michigan 1962).Google Scholar
(5)Liu, M-C.Simultaneous approximation of two additive forms. Proc. Cambridge Philos. Soc. 75 (1974), 77–82.CrossRefGoogle Scholar
(6)Liu, M-C.Simultaneous approximation of r additive forms. Trans. Amer. Math. Soc. (in press).Google Scholar