Jacob's ladders and new equivalents of the Fermat-Wiles theorem connected with some cross-bred of the formulae of Hardy-Littlewood-Ingham (1926) and of Ingham (1926)

TL;DR

This paper introduces new formulas linking zeta integrals on the critical line and strip, and combines classical formulas to produce novel equivalents of the Fermat-Wiles theorem, advancing understanding in analytic number theory.

Contribution

It presents a new formula connecting zeta integrals on the critical line with those in the critical strip, and creates new equivalents of Fermat-Wiles theorem through cross-breeding classical formulas.

Findings

New formula connecting zeta integrals on the critical line and strip

A novel equivalence of Fermat-Wiles theorem derived from classical formulas

Advances in analytic number theory connecting zeta functions and Fermat-Wiles theorem

Abstract

The main result of this paper is new formula connecting certain $zeta$-integral on the critical line with a $\zeta$-integral in the critical strip. Further, a kind of cross-breeding of the Hardy-Littlewood-Ingham formula and Ingham formula produces new $\zeta$-equivalent of the Fermat-Wiles theorem.