View in EDS

On the concavity and convexity of 1/ζ.

Saved in:
Bibliographic Details
Title: On the concavity and convexity of 1/ζ.
Authors: Alzer, Horst1 (AUTHOR) h.alzer@gmx.de, Kwong, Man Kam2 (AUTHOR) mankamkwong.math@outlook.com
Source: International Journal of Number Theory. Sep2025, Vol. 21 Issue 8, p1825-1835. 11p.
Subject Terms: *MONOTONIC functions
Abstract: Let ζ be the Riemann zeta function. In 2020, Alkan proved that 1 / ζ is strictly concave on [ 0. 2 2 , ∞). We extend this result and show that 1 / ζ is strictly concave on the maximal interval (− 2 , ∞). Moreover, we study concavity and convexity properties of 1 / ζ on (− 1 0 , − 2). Applications lead to functional inequalities involving the zeta function. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:Let ζ be the Riemann zeta function. In 2020, Alkan proved that 1 / ζ is strictly concave on [ 0. 2 2 , ∞). We extend this result and show that 1 / ζ is strictly concave on the maximal interval (− 2 , ∞). Moreover, we study concavity and convexity properties of 1 / ζ on (− 1 0 , − 2). Applications lead to functional inequalities involving the zeta function. [ABSTRACT FROM AUTHOR]
ISSN:17930421
DOI:10.1142/S1793042125500897