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Some Convexity Properties of Dirichlet Series with Positive Terms

Cerone, Pietro and Dragomir, Sever S (2005) Some Convexity Properties of Dirichlet Series with Positive Terms. Research report collection, 8 (4).

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Abstract

Some basic results for Dirichlet series ψ with positive terms via log-convexity properties are pointed out. Applications for Zeta, Lambda and Eta functions are considered. The concavity of the function 1/ψ is explored and, as a main result, it is proved that the function 1/ζ is concave on (1,∞) . As a consequence of this fundamental result it is noted that Zeta at the odd positive integers is bounded above by the harmonic mean of its immediate even Zeta values.

Item Type: Article
Uncontrolled Keywords: Dirichlet series, zeta function, lambda function, logarithmic convexity, log-convex
Subjects: FOR Classification > 0101 Pure Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 13 Feb 2012 06:31
Last Modified: 24 May 2013 04:12
URI: http://vuir.vu.edu.au/id/eprint/17581
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