G. Csordas, A. M. Odlyzko, W. Smith, and R. S. Varga, A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant Λ, ETNA (Electronic Transactions on Numerical Analysis) 1(1993), 104-111. MR 94k:11098. Zbl. 807.11059.

Dedicated to Wilhelm Niethammer on the occasion of his 60th birthday. Abstract. The de Bruijn-Newman constant Λ has been investigated extensively because the truth of the Riemann Hypothesis is equivalent to the assertion that Λ \leq 0. On the other hand, C. M. Newman conjectured that Λ \geq 0. This paper improves previous lower bounds by showing that − 5:895 10− 9 < Λ: This is done with the help of a spectacularly close pair of consecutive zeros of the Riemann zeta function.


full paper