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

Abstract

In this paper we study certain stochastic process that is generated by the Riemann-Siegel formula. Further, we construct corresponding statistical model by a way similar to those used in telecommunication. We define statistical arc length of the Riemann $Z(t)$-curve in this model and obtain an asymptotic formula for that length. This paper is English remake of our work of reference \cite{4}.

References in corpus (2)

• On the roots of the equation $Z^{\prime }(t)=0$
• Riemann hypothesis and the arc length of the Riemann $Z(t)$-curve