On the higher derivatives of Z(t) associated with the Riemann Zeta-Function

Abstract

Let $Z(t)$ be the classical Hardy function in the theory of the Riemann zeta-function. The main result in this paper is that if the Riemann hypothesis is true then for any positive integer $n$ there exists a $t_{n}>0$ such that for $t>t_{n}$ the function $Z^{(n+1)}(t)$ has exactly one zero between consecutive zeros of $Z^{(n)}(t)$.