Inequalities for Riemann’s zeta function

  • Horst Alzer

    Waldbröl, Germany


Let and be the Riemann zeta function and the von Mangoldt function, respectively. Further, let . We prove that the double-inequality

holds for all with the best possible constants

This extends and refines a recent result of Cerone and Dragomir.

Cite this article

Horst Alzer, Inequalities for Riemann’s zeta function. Port. Math. 66 (2009), no. 3, pp. 321–327

DOI 10.4171/PM/1846