Abstract
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.
Research supported by the National Science Foundation. AMS(MOS) subject classification: 30D10, 30D15, 65E05; CR:G1.m.
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© 1992 Springer-Verlag New York, Inc.
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Norfolk, T.S., Ruttan, A., Varga, R.S. (1992). A Lower Bound for the de Bruijn-Newman Constant Λ. II. In: Gonchar, A.A., Saff, E.B. (eds) Progress in Approximation Theory. Springer Series in Computational Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2966-7_17
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DOI: https://doi.org/10.1007/978-1-4612-2966-7_17
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