Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relations to the Selberg's formula (1946) and the Fermat-Wiles theorem

Abstract

In this paper we give new consequences that follow from our formula for increments of the Hardy-Littlewood integral. Main of these consequences is an $\zeta$-equivalent of the Fermat-Wiles theorem. It is expressed purely by means of the Riemann's zeta-function on the critical line and by the Jacob's ladder.