The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis

DOI10.1007/BF02142328zbMath0751.11043OpenAlexW2034985581MaRDI QIDQ1187058

Richard S. Varga, George Csordas, Arden Ruttan

Publication date: 28 June 1992

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02142328

zbMATH Keywords

numerical methodlower boundsLaguerre-Pólya classRiemann \(\zeta\)-functionde Bruijn-Newman constantRiemann HypothesisRiemann \(\xi\)-functionLaguerre inequalities

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Evaluation of number-theoretic constants (11Y60)

Related Items (9)

Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE ⋮ Constants of de Bruijn–Newman type in analytic number theory and statistical physics ⋮ On the number of non-real zeroes of a homogeneous differential polynomial and a generalisation of the Laguerre inequalities ⋮ An improved lower bound for the de Bruijn-Newman constant ⋮ Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant ⋮ Lehmer pairs of zeros, the de Bruijn-Newman constant \(\Lambda\), and the Riemann hypothesis ⋮ Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner--Pollaczek, and continuous Hahn bases ⋮ A proof of Newman’s conjecture for the extended Selberg class

Uses Software

• Algorithm 524

Cites Work

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• A new lower bound for the de Bruijn-Newman constant
• Necessary and sufficient conditions and the Riemann hypothesis
• A lower bound for the de Bruijn-Newman constant \(\Lambda\)
• Extensions of inequalities of the Laguerre and Turan type
• The roots of trigonometric integrals
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• The Riemann Hypothesis and the Turan Inequalities
• Fourier Transforms with Only Real Zeros
• On the General Hermite Cardinal Interpolation
• On inequalities of the Turán type

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