Archiv der Mathematik

, Volume 85, Issue 1, pp 70–78 | Cite as

Several types of algebraic numbers on the unit circle

Original Paper


Let A p  ⊂ C denote the set of all algebraic numbers such that α ∈ A p if and only if α is a zero of a (not necessarily irreducible) polynomial with positive rational coefficients. We give several results concerning the numbers in A p . In particular, the intersection of A p and the unit circle |z| = 1 is investigated in detail. So we determine all numbers of degree less than 6 on the unit circle which lie in the set A p . Further we show that when α is a root of an irreducible rational polynomial p(X) of degree ≠ 4 whose Galois group contains the full alternating group, α lies in A p if and only if no real root of p(X) is positive.

Mathematics Subject Classification (2000).

11R04 11R09 


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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • G. Kuba
    • 1
  1. 1.Institut für MathematikUniversität für BodenkulturWienAustria

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