Abstract
The main result in this paper, contained in Theorem 1, is a generalisation of the inequality of the arithmetic-geometric means. A result of a similar character has been proved by Siegel (2). The present result gives an improvement in the inequality in the case when the variables involved are not all distinct, whereas Siegel's result does not. The theorem is used in § 3 to obtain a result in connection with totally real and positive algebraic integers.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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1. Potential energy of totally positive algebraic integers;Journal of Mathematical Analysis and Applications;2022-12
2. Distribution of algebraic numbers;Journal für die reine und angewandte Mathematik (Crelles Journal);2011-01
3. The mean values of totally real algebraic integers;Mathematics of Computation;1984