Riemann hypothesis and the arc length of the Riemann $Z(t)$-curve
  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. 
Jan Moser
math.CA