Gram's Law

Gram's law (Hutchinson 1925; Edwards 2001, pp. 125, 127, and 171) is the tendency for zeros of the Riemann-Siegel function  to alternate with Gram points. Stated more precisely, it notes the tendency for  to hold, where  is a Gram point.

Strictly speaking, the statement "" should perhaps be called the weak Gram's law since Hutchinson (1925) used the term "Gram's law" to refer to the stronger statement that there are precisely  zeros of  between 0 and  (Edwards 2001, p. 171).

REFERENCES:

Edwards, H. M. Riemann's Zeta Function. New York: Dover, 2001.

Hutchinson, J. I. "On the Roots of the Riemann Zeta-Function." Trans. Amer. Math. Soc. 27, 49-60, 1925.