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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Sums of powers of conjugates of algebraic numbers


Author: P. E. Blanksby
Journal: Proc. Amer. Math. Soc. 49 (1975), 28-32
MSC: Primary 10F30; Secondary 12A15
MathSciNet review: 0382180
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Abstract: This note is primarily concerned with algebraic numbers which have at least one conjugate with modulus exceeding one. Theorems which give lower bounds for the maximum of the moduli of the conjugates of such algebraic numbers are connected with equivalent theorems giving lower bounds for the sums of powers of the conjugates. The results relate to some earlier work of S. Chowla, and the method used depends on one of P. Turán's main theorems on lower bounds for sums of powers of complex numbers.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0382180-5
PII: S 0002-9939(1975)0382180-5
Keywords: Algebraic numbers, conjugates
Article copyright: © Copyright 1975 American Mathematical Society