%0 Journal Article %T The validity of the analog of the Riemann hypothesis for some parts of $¦Æ(s)$ and the new formula for $¦Ð(x)$ %A Jan Moser %J Mathematics %D 2011 %I arXiv %X An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the solutions of the similar integral equations. \noindent This paper is the English version of the paper of reference \cite{1}. %U http://arxiv.org/abs/1109.0810v1