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Closed sets of algebraic numbers in complete fields

Published online by Cambridge University Press:  26 February 2010

C. J. Smyth
C. J. Smyth
Affiliation:
Trinity College, Cambridge.
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Extract

A PV-number is defined to be an algebraic integer θ, of modulus greater than one, all of whose conjugates (excluding θ itself) lie inside the unit circle. Salem [1] has shown that the set S of PV-numbers forms a closed subset of the real line.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 199 - 205
Copyright
Copyright © University College London 1970

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References

1.Salem, R., “A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan”, Duke Math. J., 11 (1944), 103–108.CrossRefGoogle Scholar
2.Kelly, J. B., “A closed set of algebraic integers”, Amer. J. Math., 72 (1950), 565–572.CrossRefGoogle Scholar
3.Chabauty, C., “Sur la répartition modulo un de certaines suites p-adiques”, C. R. Acad. Sci. Paris, 231 (1950), 465–466.Google Scholar
4.Grandet-Hugot, M., “Sur les dérivés d'un ensemble d'entiers algébriques”, C. R. Acad. Sci. Paris, 254 (1962), 2905–2906.Google Scholar
5.Pisot, C., Quelques aspects de la théorie des entiers algébriques, 2nd Edition (Université de Montréal 1966).Google Scholar
6.Senge, H. G., “Closed sets of algebraic numbers”, Duke Math. J., 34 (1967), 307–323.CrossRefGoogle Scholar
7.Cantor, D. G., “On sets of algebraic integers whose remaining conjugates lie in the unit circle”, Trans. Amer. Math. Soc., 105 (1962), 391–406.CrossRefGoogle Scholar