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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Conjugate algebraic integers in an interval
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Proc. Amer. Math. Soc. 53 (1975), 259-261 Request permission

Abstract:

The following conjecture of R. M. Robinson is proved. If $\Delta$ is a real interval of length greater than $4$, then for any sufficiently large $n$ there exists an irreducible monic polynomial of degree $n$ with integer coefficients all of whose zeros lie in $\Delta$.
References
  • Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, Monografie Matematyczne, Tom 57, PWN—Polish Scientific Publishers, Warsaw, 1974. MR 0347767
  • Raphael M. Robinson, Intervals containing infinitely many sets of conjugate algebraic integers, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 305–315. MR 0144892
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 259-261
  • MSC: Primary 12A15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0382219-7
  • MathSciNet review: 0382219