Jacob's ladders, next equivalents of the Fermat-Wiles theorem and new infinite sets of the equivalents generated by the Dirichlet's series

TL;DR

This paper introduces new equivalence sets related to Fermat-Wiles theorem and explores asymptotic links between Dirichlet series, the Riemann zeta-function, and Jacob's ladders, advancing understanding of these interconnected mathematical concepts.

Contribution

It presents novel equivalence sets for Fermat-Wiles theorem and establishes asymptotic relationships involving Dirichlet series and Jacob's ladders.

Findings

New sets of equivalents for Fermat-Wiles theorem

Asymptotic connections between Dirichlet series and zeta-function

Insights into Jacob's ladders and Dirichlet sums

Abstract

In this paper we obtain new sets of equivalents of the Fermat-Wiles theorem. Simultaneously, we obtain also asymptotic connections between the set of Dirichlet's series, certain segments of the Dirichlet's sum $\mfrak{D}(x)$, Riemann zeta-function and Jacob's ladders.