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

TL;DR

This paper introduces a stochastic model based on the Riemann-Siegel formula to analyze the statistical arc length of the Riemann Z(t)-curve, providing an asymptotic formula for its length.

Contribution

It constructs a novel statistical model for the Riemann Z(t)-curve and derives an asymptotic expression for its arc length, bridging number theory and stochastic processes.

Findings

Derived an asymptotic formula for the statistical arc length of the Riemann Z(t)-curve

Established a stochastic process model inspired by telecommunication methods

Extended previous work with a new statistical perspective on the 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}.