Jacob's ladders, our old formula (1985) and new $\zeta$-equivalent of the Fermat-Wiles theorem on two-parametric set of lemniscates of Bernoulli

TL;DR

This paper revisits a 1985 construction involving integrals of the Riemann zeta function and introduces a new $6$-equivalent of the Fermat-Wiles theorem related to lemniscates of Bernoulli, expanding the understanding of zeta function properties.

Contribution

It introduces a novel $6$-equivalent of the Fermat-Wiles theorem based on integrals over lemniscates, connecting zeta function analysis with algebraic number theory.

Findings

Constructed two integrals of Z^2(t) with asymptotically equal measures

Identified a significant excess difference between these integrals

Developed a new $6$-equivalent of Fermat-Wiles theorem

Abstract

In our paper from 1985 we have constructed two integrals of the Riemann's function $Z^2(t)$ over two disconnected sets with asymptotically equal measures such that these two integrals differ by considerably big excess. In the present paper we use the formula for that excess to construct a new $\zeta$-equivalent of the Fermat-Wiles theorem on a two-parametric set of lemniscates of Bernoulli.