Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Inequalities for the Hurwitz zeta function

Horst Alzera1

a1 Morsbacher Str. 10, 51545 Waldbröl, Germany

Abstract

Let S0308210500000652inline001 be the Hurwitz zeta function. Furthermore, let p > 1 and α ≠ 0 be real numbers and n ≥ 2 be an integer. We determine the best possible constants a(p, α, n), A(p, α, n), b(p, n) and B(p, n) such that the inequalities

S0308210500000652disp001

and
S0308210500000652disp002

hold for all positive real numbers x1,…,xn.

(Received February 19 1999)

(Accepted September 27 1999)