An inequality involving a ratio of zeta functions

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 3, Pages 92–94
DOI: 10.7546/nntdm.2018.24.3.92-94
Full paper (PDF, 133 Kb)

Details

Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Str. Kogalniceanu nr.1, 400084 Cluj, Romania

Abstract

We prove an inequality for a ratio of zeta functions. This extends a classical result (see [2]). The method is based on Dirichlet series, combined with real analysis.

Keywords

• Riemann zeta function
• Dirichlet series
• Inequalities for real functions

2010 Mathematics Subject Classification

• 11A25
• 11N37
• 26D20

References

1. Hardy, G. H., & Wright, E. M. (1964) An Introduction to the Theory of Numbers, Oxford Univ. Press.
2. Titchmarsh, E. C. (1951) The Theory of the Riemann Zeta Function, Oxford.