Microscopic interpolation formula for the Riemann $Z(t)$-function and   new algorithm for asymptotic solution of some Diophantine equation with   Leibnitz coefficients
  In this paper we use the values of the Riemann $Z(t)$-function in order to construct certain quasi-orthonormal system of vectors. On this basis we prove a formula for microscopic interpolation of the function $Z(t)$. Simultaneously we have obtained a new algorithm how to construct asymptotic solutions of Diophantine equation with Leibnitz coefficients. This paper is English version of the paper \cite{3} except the Appendix. 
Jan Moser
math.CA