Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T08:41:31.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Sums of three roots of unity. II

Published online by Cambridge University Press:  24 October 2008

A. J. Jones
A. J. Jones
Affiliation:
Trinity College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

The present paper is a sequel to a previous paper (1) in which I proved a conjecture made by R. M. Robinson concerning sums of three roots of unity. For any algebraic integer α, we denote by the maximum absolute value of α and all its algebraic conjugates. We say that α and β are equivalent if α = εβ′, where ε is some root of unity and β′ is some conjugate of β; when this happens we obviously have

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 43 - 59
Copyright
Copyright © Cambridge Philosophical Society 1969

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)Jones, A. J.Sums of three roots of unity. Proc. Cambridge Philos. Soc. 64 (1968), 673–682.CrossRefGoogle Scholar
(2)Jacobstual, E.Über Sequenzen ganzer Zahien, von denen keine zu n teilerfremd ist. I–V, Norske Vid. Selsk. Forh. (Trondheim) 33 (1960), 117–124Google Scholar
Jacobstual, E.Über Sequenzen ganzer Zahien, von denen keine zu n teilerfremd ist. I–V, Norske Vid. Selsk. Forh. (Trondheim) 33 (1960), 125–131Google Scholar
Jacobstual, E.Über Sequenzen ganzer Zahien, von denen keine zu n teilerfremd ist. I–V, Norske Vid. Selsk. Forh. (Trondheim) 33 (1960), 132–139Google Scholar
Jacobstual, E.Über Sequenzen ganzer Zahien, von denen keine zu n teilerfremd ist. I–V, Norske Vid. Selsk. Forh. (Trondheim) 34 (1961), 1–7Google Scholar
Jacobstual, E.Über Sequenzen ganzer Zahien, von denen keine zu n teilerfremd ist. I–V, Norske Vid. Selsk. Forh. (Trondheim) 34 (1961), 110–115.Google Scholar
(3)Mann, H. B.On linear relations between roots of unity. Mathematika 12 (1965), 107–117.CrossRefGoogle Scholar
(4)Conway, J. H. Trigometric Diophantino equations. (Forthcoming paper.)Google Scholar
(5)Robinson, R. M.Some conjectures about cyclotonic integers. Math. Camp. 19 (1965), 210–217.CrossRefGoogle Scholar