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Jacob's ladders, reverse iterations and new infinite set of $L_2$-orthogonal systems generated by the Riemann $\zf$-function
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abstract
It is proved in this paper that continuum set of $L_2$-orthogonal systems generated by the Riemann zeta-function on the critical line corresponds to every fixed $L_2$-orthogonal system on a fixed segment. This theorem serves as a resource for new set of integrals not accessible by the current methods in the theory of the Riemann zeta-function. \noindent Dedicated to the 100th anniversary of G.H. Hardy's fundamental theorem: the function $\zf$ has an infinite set of zeros, \cite{1}.
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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