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

2023/12/19 by Jan Moser, Moser, Jan
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.12085

openalex publication_date 2023/12/19 · openalex created_date 2023/12/22 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain number of new equivalents of the Fermat-Wiles theorem that are based on Jacob's ladders. The main of these is the D-equivalent that is generated by the Dirichlet's D(x)-function.

Related

• 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, next equivalents of the Fermat-Wiles theorem and new infinite sets of the equivalents generated by the Dirichlet's series
• 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, almost exact decomposition of certain increments of the Hardy-Littlewood integral (1918) by means of the Raabe's integral and the thirteenth equivalent 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)