Geodesic
A Generalization of the Inequality of the Arithmetic-Geometric Means
Glasgow mathematical journal, Tome 2 (1956) no. 4, pp. 149-158

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Hunter, John. A Generalization of the Inequality of the Arithmetic-Geometric Means. Glasgow mathematical journal, Tome 2 (1956) no. 4, pp. 149-158. doi: 10.1017/S2040618500033268
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[(1)] (1)Schur, I., “Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten,” Math. Zeitschrift, 1 (1918), 377–402. Google Scholar

[(2)] (2)Siegel, C. L., “The trace of totally positive and real algebraic integers,” Annals of Math., (2) 46, (1945), 302–312. Google Scholar

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