Multiple positivity and the Riemann zeta-function

DOI10.1007/BF03321628zbMath1147.30020arXivmath/0505174MaRDI QIDQ2467657

Olga M. Katkova

Publication date: 28 January 2008

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505174

zbMATH Keywords

Laguerre-Pólya classPólya frequency sequencesmultiple positivity sequences

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Representations of entire functions of one complex variable by series and integrals (30D10) Special classes of entire functions of one complex variable and growth estimates (30D15)

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Preservers of totally positive kernels and Pólya frequency functions ⋮ Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ On the concavity properties of certain arithmetic sequences and polynomials ⋮ On some Turán-type inequalities ⋮ Higher order Turán inequalities for the partition function ⋮ Laguerre multiplier sequences and sector properties of entire functions

Cites Work

• Moment inequalities and the Riemann hypothesis
• Jensen polynomials and the Turán and Laguerre inequalities
• Necessary and sufficient conditions and the Riemann hypothesis
• On the generating functions of totally positive sequences. I
• A note on multiply positive sequences and the Descartes rule of signs
• On the zeros of the generating functions of multiply positive sequences and functions
• The Riemann Hypothesis and the Turan Inequalities
• Higher order Turán inequalities
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