An improved bound for the de Bruijn-Newman constant

The Riemann hypothesis is equivalent to the conjecture that the de Bruijn-Newman constant Λ satisfies Λ ≤ 0. However, so far all the bounds that have been proved for Λ go in the other direction, and provide support for the conjecture of Newman that Λ ≥ 0. This paper shows how to improve previous lower bounds and prove that -2.7 · 10^-9 < Λ. This can be done using a pair of zeros of the Riemann zeta function near zero number 10²⁰ that are unusually close together. The new bound provides yet more evidence that the Riemann hypothesis, if true, is just barely true.