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Jacob's ladders, logarithmic modification of the Hardy-Littlewood integral (1918), Titchmarsh's $\Omega$-theorem (1928) and new point of contact with the Fermat-Wiles theorem
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In this paper we obtain two new points of contact between Jacob's ladders and Fermat-Wiles theorem. They are generated by a logarithmic modification of the Hardy-Littlewood integral. Furthermore, we present a kind of asymptotic laws of conservation for a set of areas connected with above mentioned modification of the Hardy-Littlewood integral.
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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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