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Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918), the classical Dirichet's sum of divisors (1849) and their relationship with the Fermat-Wiles theorem
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abstract
In this paper we obtain number of new equivalents of the Fermat-Wiles theorem that are based on Jacob's ladders. The main of these is the $D$-equivalent that is generated by the Dirichlet's $D(x)$-function.
Forward citations
Cited by 4 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 new $\zeta$-functionals and corresponding $\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\zeta$-pulses
The paper restates Moser's ζ-functional as sums over zero-to-zero intervals and derives 'ζ-equivalents' of Fermat's Last Theorem that are tautological consequences of the claimed asymptotic.
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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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Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new $\zeta$-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence
The paper derives zeta-function expressions that equal x for every x>0, then plugs in Fermat rationals, so its "equivalents" of Fermat's Last Theorem are identities rather than new mathematics.
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