Jacob's ladders and the equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood formula (1921)

Abstract

In this paper we prove that the 105 years old Lemma 18 of Hardy and Littlewood from theirs fundamental paper \cite{2} is able to generate, for example, a continuum set of new $\zeta$-equivalents of the Fermat-Wiles theorem.