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

In this paper we obtain new $\zeta$-equivalents of the Fermat-Wiles theorem. These are generated by our asymptotic formulae (1981) which brought $33.3\mathrm{\%}$ improvement of the Hardy-Littlewood exponent $\frac{1}{4}$ dated 1918.