A Lower Bound for the de Bruijn-Newman Constant Λ. II
A new constructive method is given here for determining lower bounds for the de Bruijn-Newman constant Λ, which is related to the Riemann Hypothesis. This method depends on directly tracking real and nonreal zeros of an entire function F λ(z), where λ < 0, instead of finding, as was previously done, nonreal zeros óf associated Jensen polynomials. We apply this new method to obtain the new lower bound for Λ,-0.385 < Λ, which improves previous published lower bounds of —50 and —5.
KeywordsEntire Function Simple Zero Real Zero Riemann Hypothesis Computational Complex Analysis
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- T.S. Norfolk, A. Ruttan, and R.S. Varga, A detailed numerical examination of the tracking of zeros of F λ(z) to produce lower bounds for the de Bruijn-Newman constant Λ, Technical Report of the Institute for Computational Mathematics, 1990, Kent State University, Kent, OH 44242.Google Scholar
- G. Pólya, Über die algebraisch-funktionen Untersuchungen von J.L.W.V. Jensen, Kgl. Danske Vid Sel. Math.-Fys. Medd. 7(1927), 3–33.Google Scholar
- H.J.J, te Riele, A new lower bound for the de Bruijn-Newman constant, Numer. Math, (to appear).Google Scholar