*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Let be the Xi Function defined by

(1) |

(2) |

(3) |

**References**

Csordas, G.; Odlyzko, A.; Smith, W.; and Varga, R. S. ``A New Lehmer Pair of Zeros and a New Lower Bound for the
de Bruijn-Newman Constant.'' *Elec. Trans. Numer. Analysis* **1**, 104-111, 1993.

Csordas, G.; Smith, W.; and Varga, R. S. ``Lehmer Pairs of Zeros, the de Bruijn-Newman Constant and the Riemann
Hypothesis.'' *Constr. Approx.* **10**, 107-129, 1994.

de Bruijn, N. G. ``The Roots of Trigonometric Integrals.'' *Duke Math. J.* **17**, 197-226, 1950.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/dbnwm/dbnwm.html

Newman, C. M. ``Fourier Transforms with only Real Zeros.'' *Proc. Amer. Math. Soc.* **61**, 245-251, 1976.

© 1996-9

1999-05-24