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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
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abstract
In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are $\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.
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Cited by 2 Pith papers
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Jacob's ladders, $\zeta$-transformation of the Fourier orthogonal system (2014) and new infinite sets of $\zeta$-equivalents of the Fermat-Wiles theorem
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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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
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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