Higher order Turán inequalities for the Riemann $\xi$-function

DOI10.1090/S0002-9939-2010-10515-4zbMath1214.11092OpenAlexW2012948663MaRDI QIDQ3085065

Fábio Rodrigues Lucas, Dimitar K. Dimitrov

Publication date: 28 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10515-4

zbMATH Keywords

Laguerre-Pólya classRiemann \(\xi\)-functionTurán inequalitiesJensen polynomialsMacLaurin coefficients

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other functions defined by series and integrals (33E20)

Related Items (16)

Jensen polynomials for holomorphic functions ⋮ Laguerre inequalities for discrete sequences ⋮ Higher order Turán inequalities for Boros-Moll sequences ⋮ A simple proof of higher order Turán inequalities for Boros-Moll sequences ⋮ Radii of starlikeness and convexity of some \(q\)-Bessel functions ⋮ Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ Zero-free regions near a line ⋮ Properties arising from Laguerre-Pólya class for the Boros-Moll numbers ⋮ Inequalities associated with the Baxter numbers ⋮ Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers ⋮ An inequality for coefficients of the real-rooted polynomials ⋮ Zeros of Jensen polynomials and asymptotics for the Riemann xi function ⋮ Higher order Turán inequalities for the partition function ⋮ The Jensen-Pólya program for various \(L\)-functions ⋮ Jensen polynomials for the Riemann xi-function ⋮ Heine representations and monotonicity properties of determinants and Pfaffians

Cites Work

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• Necessary and sufficient conditions and the Riemann hypothesis
• Generalization of a formula of Hayman and its application to the study of Riemann's zeta function
• Corrections and completion of the paper 'Generalization fo a formula of Hayman'
• A Generalisation of Stirling's Formula.
• The Riemann Hypothesis and the Turan Inequalities
• Higher order Turán inequalities
• Conjectures and theorems in the theory of entire functions

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