A lower bound for the de Bruijn-Newman constant \(\Lambda\)

DOI10.1007/BF01400887zbMath0663.65017MaRDI QIDQ1114299

Richard S. Varga, Timothy S. Norfolk, George Csordas

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133248

zbMATH Keywords

error estimateslower boundRiemann hypothesisde Bruijn-Newman constantzeros of polynomialhigh-precision numerical calculations

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) 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

The Laguerre inequalities and the zeros of the Riemann ξ-function, On the de Bruijn-Newman constant, Classification theorems for operators preserving zeros in a strip, Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function, THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE, Lehmer Pairs Revisited, Constants of de Bruijn–Newman type in analytic number theory and statistical physics, A new lower bound for the de Bruijn-Newman constant, Necessary and sufficient conditions and the Riemann hypothesis, The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis, 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, The GHS inequality and the Riemann hypothesis, 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
• Algorithm 493

Cites Work

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• Asymptotic upper and lower bounds for results of extrapolation methods
• Recherches sur la méthode de Graeffe et les zéros des polynômes et des séries de Laurent
• 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