Jacob's ladders, $\zeta$-transformation of the Fourier orthogonal system (2014) and new infinite sets of $\zeta$-equivalents of the Fermat-Wiles theorem

In this paper we obtain new infinite sets of $\zeta$-equivalents of the Fermat-Wiles theorem based on the elementary Fourier orthogonal system, Riemann’s zeta-function and Jacob’s ladders.