Jacob's ladders, our asymptotic formulae (1981) and next $\zeta$-equivalents of the Fermat-Wiles theorem together with decomposition and synthesis of the Riemann's $\zeta$-oscillators

TL;DR

This paper introduces new $\zeta$-equivalents of the Fermat-Wiles theorem derived from asymptotic formulae, improving classical exponents and offering insights into the structure of Riemann's $\zeta$-oscillators.

Contribution

It presents novel $\zeta$-equivalents based on 1981 asymptotic formulae, enhancing previous results and connecting to the theory of Riemann's $\zeta$-oscillators.

Findings

New $\zeta$-equivalents of Fermat-Wiles theorem

33.3% improvement of Hardy-Littlewood exponent

Decomposition and synthesis of Riemann's $\zeta$-oscillators

Abstract

In this paper we obtain new $\zeta$-equivalents of the Fermat-Wiles theorem. These are generated by our asymptotic formulae (1981) which brought $33.3\%$ improvement of the Hardy-Littlewood exponent $\frac 14$ dated 1918.