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

Abstract

On Riemann hypothesis it is proved in this paper that the arc length of the Riemann $Z$-curve is asymptotically equal to the double sum of local maxima of the function $Z(t)$ on corresponding segment. This paper is English remake of our paper \cite{9}, with short appendix concerning new integral generated by Jacob's ladders added.

References in corpus (1)

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

Cited by in corpus (2)

• Jacob's ladders and properties of complete additivity and complete multiplicativity in the set of reverse iterated integrals (energies)
• On statistical arc length of the Riemann $Z(t)$-curve