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

TL;DR

This paper demonstrates that a historical lemma by Hardy and Littlewood can generate a continuum of new equivalences related to the Fermat-Wiles theorem using the Hardy-Littlewood formula.

Contribution

It reveals a novel application of Hardy and Littlewood's Lemma 18 to produce infinitely many new $$-equivalents of the Fermat-Wiles theorem.

Findings

Generated a continuum set of new $$-equivalents

Linked Hardy-Littlewood lemma to Fermat-Wiles theorem

Extended classical lemma to modern number theory

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.