Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-16T07:14:41.785Z Has data issue: false hasContentIssue false
  • English
  • Français

On the measure of totally real algebraic integers

Published online by Cambridge University Press:  09 April 2009

C. J. Smyth
C. J. Smyth
Affiliation:
Department of Mathematics, James Cook, University Townsville, Queensland, Australia4811
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.

For totally real algebraic integers x of degree D(x), we examine the stucture of the set of values M(x)1D(x). where M(x) is the measure of x. We find a small limit point λ of this set, and show that the set is everywhere dense in (λ x).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 137 - 149
Copyright
Copyright © Australian Mathematical Society 1980

References

Albert, A. A. (1965). Fundamental concepts of higher algebra (University of Chicago Press).Google Scholar
Boyd, D. W. (1978). ‘Variations on a theme of Kronecker’, Canad. Math. Bull. 21 (2). 129–133.CrossRefGoogle Scholar
Dobrowolski, E. (1979), ‘On a question of Lehmer and the number of irreducible factors of a polynomial’, Acta Arith. 34, 391–401.CrossRefGoogle Scholar
Hardy, G. M. and Wright, E. M. (1960), An introduction to the theory of numbers, 4th ed. (Oxford).Google Scholar
Kuipers, L. and Niederreiter, H. (1974), Uniform distribution of sequences (Wiley).Google Scholar
Mignotte, M. (1978), ‘Entiers algébriques dont les conjugués sont proches du cercle unité, Séminaire Delange-Pisot-Poitou (Théorie des nombres), 19e année, No. 39.Google Scholar
Schinzel, A.(1973), ‘On the product of the conjugates outside the unit circle of an algebraic number’, Acta Arith. 24, 385–399.CrossRefGoogle Scholar
Stewart, C. L. (1978), ‘Algebraic integers whose conjugates lie near the unit circle’. Bull. Soc. Math. France 106. 169–176.CrossRefGoogle Scholar