Zeros of Jensen polynomials and asymptotics for the Riemann xi function

DOI10.1007/s40687-020-00240-5zbMath1479.11146arXiv2007.13582OpenAlexW3178875170WikidataQ114218945 ScholiaQ114218945MaRDI QIDQ2042088

Cormac O'Sullivan

Publication date: 28 July 2021

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.13582

zbMATH Keywords

Riemann xi function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (9)

Jensen polynomials for holomorphic functions ⋮ Limits of Jensen polynomials for partitions and other sequences ⋮ Detailed asymptotic expansions for partitions into powers ⋮ The Laguerre-Pólya class and combinatorics. Abstracts from the workshop held March 13--19, 2022 ⋮ Stirling's approximation and a hidden link between two of Ramanujan's approximations ⋮ A note on the zeros of Jensen polynomials ⋮ De Moivre and Bell polynomials ⋮ Jensen polynomials are not a plausible route to proving the Riemann hypothesis ⋮ Positivity of the determinants of the partition function and the overpartition function

Cites Work

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• Jensen polynomials and the Turán and Laguerre inequalities
• Necessary and sufficient conditions and the Riemann hypothesis
• Laguerre polynomials as Jensen polynomials of Laguerre-Pólya entire functions
• On the number of nonreal zeros of real entire functions and the Fourier-Pólya conjecture
• Revisiting the saddle-point method of Perron
• The Jensen-Pólya program for various \(L\)-functions
• An asymptotic formula for the Taylor coefficients of the function $ \xi(s)$
• Laguerre multiplier sequences and sector properties of entire functions
• Asymptotic estimation of $\xi ^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades
• Higher order Turán inequalities for the Riemann $\xi$-function
• The Riemann Hypothesis and the Turan Inequalities
• Jensen polynomials for the Riemann zeta function and other sequences

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