Jacob's ladders, point of contact of the remainder in the prime-number law with the Fermat-Wiles theorem and multiplicative puzzles on some sets of integrals

TL;DR

This paper explores the connections between the Riemann hypothesis, Ingham integrals, and Fermat-Wiles theorem, proposing new functionals and equivalents that deepen understanding of prime number distribution and related puzzles.

Contribution

It introduces new functionals and $P ext{-}\zeta$-equivalents of Fermat-Wiles theorem based on increments of Ingham integrals, assuming the Riemann hypothesis.

Findings

Existence of specific Ingham integral increments under RH

New $P ext{-}\zeta$-equivalents of Fermat-Wiles theorem

Enhanced understanding of prime number law and related puzzles

Abstract

In this paper we prove, on the Riemann hypothesis, the existence of such increments of the Ingham integral (1932) that generate new functionals together with corresponding new $P\zeta$-equivalents of the Fermat-Wiles theorem. We obtain also new results in this direction.