Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new $\zeta$-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence

TL;DR

This paper introduces three new $oldsymbol{ ext{ extit{ extzeta}}}$-equivalents of Fermat-Wiles theorem derived from asymptotic formulas related to Titchmarsh's hypothesis, connecting classical number theory conjectures with modern analytical methods.

Contribution

It presents novel $oldsymbol{ ext{ extzeta}}}$-equivalents of Fermat-Wiles theorem based on prior asymptotic formulas, advancing the analytical approach to Fermat's Last Theorem.

Findings

Three new $oldsymbol{ ext{ extzeta}}}$-equivalents of Fermat-Wiles theorem

Derived from asymptotic formulas related to Titchmarsh's hypothesis

Connections established between Fermat's rationals and Gram's sequence

Abstract

In connection of our proof (1980) of the Titchmarsh's hypothesis (1934), we have obtained two asymptotic formulae (1991). In this paper we obtain three new $\zeta$-equivalents of the Fermat-Wiles theorem based on the mentioned asymptotic formulae.