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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

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arxiv 2306.07648 v2 pith:S7M6BV3B submitted 2023-06-13 math.CA math.NT

Jan Moser This is my paper · ORCID
classification math.CAmath.NT
keywords consequencesfermat-wilesformulahardy-littlewoodincrementsintegraljacobtheorem
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abstract

In this paper we give new consequences that follow from our formula for increments of the Hardy-Littlewood integral. Main of these consequences is an $\zeta$-equivalent of the Fermat-Wiles theorem. It is expressed purely by means of the Riemann's zeta-function on the critical line and by the Jacob's ladder.

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  1. Jacob's ladders and three new equivalents of the Fermat-Wiles theorem and an infinite set of these equivalents that are independent on the Jacob's ladders

    math.NT 2024-12 reject novelty 2.0 of 10

    The paper restates Fermat's Last Theorem as the condition that certain normalized integral averages of Dirichlet series do not equal 1, but the restatement carries no new mathematical content.

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