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A Generalization of the Inequality of the Arithmetic-Geometric Means

Published online by Cambridge University Press:  18 May 2009

John Hunter
John Hunter
Affiliation:
The University Glasgow
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Extract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 4 , February 1956 , pp. 149 - 158
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

REFERENCES

(1)Schur, I., “Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten,” Math. Zeitschrift, 1 (1918), 377–402.Google Scholar
(2)Siegel, C. L., “The trace of totally positive and real algebraic integers,” Annals of Math., (2) 46, (1945), 302–312.Google Scholar