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- De_Bruijn–Newman_constant abstract "The De Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zeros of a certain function H(λ, z), where λ is a real parameter and z is a complex variable. H has only real zeros if and only if λ ≥ Λ. The constant is closely connected with Riemann's hypothesis concerning the zeros of the Riemann zeta-function. In brief, the Riemann hypothesis is equivalent to the conjecture that Λ ≤ 0.De Bruijn showed in 1950 that H has only real zeros if λ ≥ 1/2, and moreover, that if H has only real zeros for some λ, H also has only real zeros if λ is replaced by any larger value. Newman proved in 1976 the existence of a constant Λ for which the "if and only if" claim holds; and this then implies that Λ is unique. Newman conjectured that Λ ≥ 0, an intriguing counterpart to the Riemann hypothesis. Serious calculations on lower bounds for Λ have been made since 1988 and—as can be seen from the table—are still being made:Since is just the Fourier transform of then H has the Wiener–Hopf representation:which is only valid for lambda positive or 0, it can be seen that in the limit lambda tends to zero then for the case Lambda is negative then H is defined so:where A and B are real constants.".
- De_Bruijn–Newman_constant wikiPageID "45265".
- De_Bruijn–Newman_constant wikiPageRevisionID "605602706".
- De_Bruijn–Newman_constant title "de Bruijn–Newman Constant".
- De_Bruijn–Newman_constant urlname "deBruijn-NewmanConstant".
- De_Bruijn–Newman_constant subject Category:Analytic_number_theory.
- De_Bruijn–Newman_constant subject Category:Mathematical_constants.
- De_Bruijn–Newman_constant comment "The De Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zeros of a certain function H(λ, z), where λ is a real parameter and z is a complex variable. H has only real zeros if and only if λ ≥ Λ. The constant is closely connected with Riemann's hypothesis concerning the zeros of the Riemann zeta-function.".
- De_Bruijn–Newman_constant label "Constante de De Bruijn-Newman".
- De_Bruijn–Newman_constant label "Costante di de Bruijn-Newman".
- De_Bruijn–Newman_constant label "De Bruijn–Newman constant".
- De_Bruijn–Newman_constant label "Stała de Bruijna-Newmana".
- De_Bruijn–Newman_constant label "德布鲁因-纽曼常数".
- De_Bruijn–Newman_constant sameAs De_Bruijn%E2%80%93Newman_constant.
- De_Bruijn–Newman_constant sameAs Constante_de_De_Bruijn-Newman.
- De_Bruijn–Newman_constant sameAs Costante_di_de_Bruijn-Newman.
- De_Bruijn–Newman_constant sameAs Stała_de_Bruijna-Newmana.
- De_Bruijn–Newman_constant sameAs Q2248459.
- De_Bruijn–Newman_constant sameAs Q2248459.
- De_Bruijn–Newman_constant wasDerivedFrom De_Bruijn–Newman_constant?oldid=605602706.