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

2025/06/02 by Jan Moser, Moser, Jan · 1 citation
Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.01706

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

In connection of our proof (1980) of the Titchmarsh's hypothesis (1934), we have obtained two asymptotic formulae (1991). In this paper we obtain three new ζ-equivalents of the Fermat-Wiles theorem based on the mentioned asymptotic formulae.

Citations

• Jacob's ladders, new equivalent of the Fermat-Wiles theorem generated by certain cross-breed of Ingham and Heath-Brown formula (1979) and some chains of equivalents
• 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)
• 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 and vector operator producing new generations of L₂-orthogonal systems connected with the Riemann's ζ(\frac 12+it) function
• Jacob's ladders, reverse iterations and new infinite set of L₂-orthogonal systems generated by the Riemann \zf-function
• Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations

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

Related

• 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, our asymptotic formulae (1981) connected with the equation Z'(t)=0 as a base for new ζ-equivalents of the Fermat-Wiles theorem and some other results
• Jacob's ladders, next equivalents of the Fermat-Wiles theorem and new infinite sets of the equivalents generated by the Dirichlet's series
• 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 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)