On the roots of the equation $Z^{\prime }(t)=0$

Abstract

We have proved in this paper that the Lindel\" of hypothesis generates essential contraction of distances between consecutive odd-order zeros of the function $Z^{\prime }(t)$. This paper is the translation of the paper \cite{11} into the English except part 8 that we added in order to point out the I. M. Vinogradov' scepticism on possibilities of the method of trigonometric sums.

Cited by in corpus (2)

• Riemann hypothesis and the arc length of the Riemann $Z(t)$-curve
• On statistical arc length of the Riemann $Z(t)$-curve