LEHMER PAIRS OF ZEROS, THE DEBRUIJN-NEWMAN CONSTANT-LAMBDA, AND THE RIEMANN-HYPOTHESIS

We give here a rigorous formulation for a pair of consecutive simple p ositive zeros of the function H-0 (which is closely related to the Rie mann xi-function) to be a ''Lehmer pair'' of zeros of H-0. With this f ormulation, we establish that each such pair of zeros gives a lower bo und for the de Bruijn-Newman constant A (where the Riemann Hypothesis is equivalent to the assertion that LAMBDA less-than-or-equal-to 0). W e also numerically obtain the following new lower bound for LAMBDA: -4 .379 . 10(-6) < LAMBDA.