Science Fair Project Encyclopedia
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 |
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details