THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE

DOI10.1017/fmp.2020.6zbMath1454.11158arXiv1801.05914OpenAlexW3016082228WikidataQ112628824 ScholiaQ112628824MaRDI QIDQ5108412

Brad Rodgers, Terence C. Tao

Publication date: 4 May 2020

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.05914

zbMATH Keywords

Riemann hypothesisde Bruijn-Newman constantNewman's conjecturesuper-exponentially decaying function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (19)

Dynamics of KPI lumps ⋮ Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function ⋮ Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations ⋮ Small gaps and small spacings between zeta zeros ⋮ Zero-free regions near a line ⋮ Exact solution of interacting particle systems related to random matrices ⋮ Constants of de Bruijn–Newman type in analytic number theory and statistical physics ⋮ Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman ⋮ Is the Riemann Zeta Function in a Short Interval a 1-RSB Spin Glass? ⋮ Superimposing theta structure on a generalized modular relation ⋮ Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant ⋮ Exploring the toolkit of Jean Bourgain ⋮ The Riemann hypothesis is true up to 3·1012 ⋮ Variants on Andrica's conjecture with and without the Riemann hypothesis ⋮ Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis ⋮ Jensen polynomials are not a plausible route to proving the Riemann hypothesis ⋮ Viscous Marangoni Flow Driven by Insoluble Surfactant and the Complex Burgers Equation ⋮ 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

• dbn_upper_bound

Cites Work

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• A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant \(\Lambda\)
• Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant
• On the de Bruijn-Newman constant
• Newman's conjecture in function fields
• The roots of trigonometric integrals
• Lehmer Pairs Revisited
• An improved lower bound for the de Bruijn-Newman constant
• ON THE DISTRIBUTION OF GAPS BETWEEN ZEROS OF THE ZETA-FUNCTION
• A Note on Gaps between Zeros of the Zeta Function
• Fourier Transforms with Only Real Zeros
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• Equivalents of the Riemann Hypothesis
• An improved bound for the de Bruijn-Newman constant

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