De Bruijn-Newman constant?

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The title of this article is shown beginning with a capital letter due to technical restrictions. The correct title is de Bruijn-Newman constant.

The de Bruijn-Newman constant, denoted by Λ, is a mathematical constant and is 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 on the zeroes of the general Euler-Riemann's ζ-function. In brief, the Riemann hypothesis is equivalent to the conjecture that Λ ≤ 0.

De Bruijn in 1950 showed that Λ ≤ 1/2, according to Newman's work, who first estimated it would be Λ ≥ 0. Serious calculations on Λ have been made since 1988 and are still being made as we see from the table:

Year	Lower bound on Λ
1988	-50
1991	-5
1990	-0.385
1994	-4.379 · 10 -6
1993	-5.895 · 10 -9
2000	-2.7 · 10 -9

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