Jacob's ladders, Hardy-Littlewood integral (1918) and new asymptotic functional equations for Euler's Gamma function together with the tenth equivalent of the Fermat-Wiles theorem

Jan Moser

Jacob's ladders, Hardy-Littlewood integral (1918) and new asymptotic functional equations for Euler's Gamma function together with the tenth equivalent of the Fermat-Wiles theorem

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arxiv 2403.17522 v1 pith:CKLNPL2N submitted 2024-03-26 math.NT math.CA

Jan Moser This is my paper · ORCID

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keywords gammafunctionalequivalenteulerfermat-wilesfunctionhardy-littlewoodintegral

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abstract

In this paper new $\Gamma$-functional is constructed upon the basis of the set of almost linear increments of the Hardy-Littlewood integral. This functional generates a $\Gamma$-equivalent of the Fermat-Wiles theorem and also new set of factorization formulae for Euler's $\Gamma$-function.

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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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