Charles Newman [MR 55 #7944],
building on work of deBruijn [
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 .
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