Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis |
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| Authors: | George Csordas Wayne Smith Richard S Varga |
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| Institution: | 1. Department of Mathematics, University of Hawaii, 96822, Honolulu, Hawaii, USA
2. Institute for Computational Mathematics, Kent State University, 44242, Kent, Ohio, USA
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| Abstract: | We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH
0 (which is closely related to the Riemann  -function) to be a  Lehmer pair of zeros ofH
0. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant  (where the Riemann Hypothesis is equivalent to the assertion that  0). We also numerically obtain the following new lower bound for :
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