Charles Newman [MR 55 #7944],
building on work of deBruijn [
MR 12,250]
defined

where

Note that

He proved that there exists a constant (with ) such that has only real zeros if and only if . RH is equivalent to the assertion that .

The constant (which Newman conjectured is equal to 0) is now called the deBruijn-Newman constant. A. Odlyzko [ MR 2002a:30046] has recently proven that .

Back to the
main index
for The Riemann Hypothesis.