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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

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arxiv 2407.11458 v1 pith:7BRGVXU7 submitted 2024-07-16 math.CA math.NT

Jan Moser This is my paper · ORCID
classification math.CAmath.NT
keywords integralalmostcertaindecompositionequivalentexactfermat-wileshardy-littlewood
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In this paper we use our theory of Jacob's ladders on the Raabe's integral to obtain: (i) The thirteenth equivalent of the Fermat-Wiles theorem, as well as (ii) almost exact decomposition of certain elements of continuum set of increments of the Hardy-Littlewood integral.

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  1. Jacob's ladders, $\zeta$-transformation of the Fourier orthogonal system (2014) and new infinite sets of $\zeta$-equivalents of the Fermat-Wiles theorem

    math.NT 2025-07 reject novelty 4.0 of 10

    A zeta-weighted integral limit is shown to equal (x^n+y^n)/z^n exactly, making 'limit not equal 1' a verbatim restatement of Fermat's Last Theorem.

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