Sums of powers of conjugates of algebraic numbers-Reference-Cited by-同舟云学术

Sums of powers of conjugates of algebraic numbers

Published:1975 Issue:1 Volume:49 Page:28-32
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Blanksby P. E.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1975-049-01/S0002-9939-1975-0382180-5/S0002-9939-1975-0382180-5.pdf

Reference5 articles.

1. Algebraic integers near the unit circle;Blanksby, P. E.;Acta Arith.,1971

2. On polynomials all of whose roots lie on the unit circle;Chowla, S.;J. Reine Angew. Math.,1966

3. L. Kronecker, Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten, J. Reine Angew. Math. 53 (1857), 173-175.

4. Generalisations of Turán’s main theorems on lower bounds for sums of powers;Van der Poorten, A. J.;Bull. Austral. Math. Soc.,1970

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