Jacob's ladders, our asymptotic formulae (1981) connected with the equation $Z^{\prime }(t)=0$ as a base for new $\zeta$-equivalents of the Fermat-Wiles theorem and some other results

Abstract

In this paper we obtain new functionals and corresponding $\zeta$-equivalents of the Fermat-Wiles theorem. These are generated by our asymptotic formulae (1981) for the function $Z^{\prime }(t)$ which we are now using to prove essential influence of the Lindel\" of hypothesis on the distribution of the roots of odd order of the equation $Z^{\prime }(t)=0$.