Multiple positivity and the Riemann zeta-function

Olga M. Katkova

Multiple positivity and the Riemann zeta-function

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arxiv math/0505174 v1 pith:HPKHR4HO submitted 2005-05-10 math.CV math.NT

Olga M. Katkova This is my paper · ORCID

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keywords sequencesolyapositiveriemannfrequencyfunctionmultiplyzeta-

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abstract

In the paper it is discussed the relations of the Riemann $\zeta-$function to classes of generating functions of multiply positive sequences according to Schoenberg (also called P\'olya frequency sequences). Key words: multiply positive sequences, totally positive sequences, P\'olya frequency sequences, Laguerre-P\'olya class, Riemann $\zeta-$function.

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An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients
math.NT 2026-07 accept novelty 7.0 of 10

For every r ≥ 2 and k ≥ 10^18 r^3, the consecutive Toeplitz minor D_{r,k} of the Riemann xi coefficients is strictly positive, proved without using verified zeta zeros.

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