A new lower bound for the de Bruijn-Newman constant

Abstract

Strong numerical evidence is presented for a new lower bound for the so-called de Bruijn-Newman constant. This constant is related to the Riemann hypothesis. The new bound, ?5, is suggested by high-precision floatingpoint computations, with a mantissa of 250 decimal digits, of i) the coefficients of a so-called Jensen polynomial of degree 406, ii) the so-called Sturm sequence corresponding to this polynomial which implies that it has two complex zeros, and iii) the two complex zoros of this polynomial. Aproof of the new bound could be given if one would repeat the computations i) and iii) with a floatingpoint accuracy of at least 2600 decimal digits.