Lehmer pairs of zeros, the de Bruijn-Newman constant \(\Lambda\), and the Riemann hypothesis

DOI10.1007/BF01205170zbMath0792.30020OpenAlexW2080252578MaRDI QIDQ1322601

Wayne Smith, Richard S. Varga, George Csordas

Publication date: 5 May 1994

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01205170

zbMATH Keywords

Riemann hypothesisde Bruijn-Newman constantLehmer pair

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) 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) Evaluation of number-theoretic constants (11Y60)

Related Items (17)

Dynamics of KPI lumps ⋮ Analytic Solutions of the Heat Equation ⋮ Classification theorems for operators preserving zeros in a strip ⋮ Lehmer pairs and derivatives of Hardy's \(Z\)-function ⋮ Newman's conjecture in various settings ⋮ Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE ⋮ Motion of Lee-Yang zeros ⋮ Lehmer Pairs Revisited ⋮ Constants of de Bruijn–Newman type in analytic number theory and statistical physics ⋮ Notes on Low discriminants and the generalized Newman conjecture ⋮ Newman's conjecture in function fields ⋮ Early work of N. G. (Dick) de Bruijn in analysis and some of my own ⋮ 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 ⋮ 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

Cites Work

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• On the roots of the Riemann zeta-function
• 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 \(\Lambda\)
• The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis
• 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

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