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

TL;DR

This paper introduces new infinite sets of $$-equivalents of the Fermat-Wiles theorem using Fourier orthogonal systems, Riemann's zeta-function, and Jacob's ladders, advancing the understanding of these mathematical structures.

Contribution

It presents novel $$-equivalents of the Fermat-Wiles theorem derived from elementary Fourier systems and Jacob's ladders, expanding the theoretical framework.

Findings

New infinite $$-equivalents of Fermat-Wiles theorem

Application of Fourier orthogonal systems and Jacob's ladders

Enhanced connections between zeta-function and number theory

Abstract

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.