Sharp inequalities for the Hurwitz zeta function

We prove the following double-inequality for the Hurwitz zeta function zeta(p, a) = Sigma(v=0)(infinity)(v + a)(-p). Let m and n be integers with m > n >= 0 and let a be a positive real number. Then we have for all real numbers P > 1: [GRAPHICS] Both bounds are best possible. Our theorem extends and refines a result of Bennett [2].