Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24497
Title: On the concavity of Dirichlet's eta function and related functional inequalities
Authors: Alzer, H
Kwong, MK
Issue Date: 2015
Source: Journal of number theory, 2015, v. 151, p. 172-196
Abstract: We prove the strict concavity of Dirichlet's eta function η(s)=∑j=1∞(-1)j-1js on (0, ∞). This extends a result of Wang, who proved in 1998 that η is strictly logarithmically concave on (0, ∞).Several new inequalities satisfied by η are also presented. Among them is the double-inequality. log 2<η(x)1/xη(y)1/yη(xy)1/xy<1, for all x, y∈. (1, ∞). Both bounds are sharp.
Keywords: Concavity
Dirichlet's eta function
Functional inequalities
Publisher: Academic Press Inc.
Journal: Journal of Number Theory 
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.12.009
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