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)

2025/01/07 by Jan Moser, Moser, Jan · 2 citations
Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2501.03646

openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Jacob's ladders, ζ-transformation of the Fourier orthogonal system (2014) and new infinite sets of ζ-equivalents of the Fermat-Wiles theorem
• Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new ζ-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence

Related

• Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relations to the Selberg's formula (1946) and the Fermat-Wiles theorem
• Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new ζ-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence
• Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem
• Jacob's ladders, our asymptotic formulae (1981) and next ζ-equivalents of the Fermat-Wiles theorem together with decomposition and synthesis of the Riemann's ζ-oscillators
• Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918), the classical Dirichet's sum of divisors (1849) and their relationship with the Fermat-Wiles theorem