TOPICS
Search

Gram's Law


GramsLaw

Gram's law (Hutchinson 1925; Edwards 2001, pp. 125, 127, and 171) is the tendency for zeros of the Riemann-Siegel function Z(t) to alternate with Gram points. Stated more precisely, it notes the tendency for (-1)^nZ(g_n)>0 to hold, where g_n is a Gram point.

Strictly speaking, the statement "(-1)^nZ(g_n)>0" 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 n+1 zeros of Z(t) between 0 and g_n (Edwards 2001, p. 171).


See also

Gram Block, Gram Point, Lehmer's Phenomenon, Riemann-Siegel Functions

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Gram's Law

Cite this as:

Weisstein, Eric W. "Gram's Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GramsLaw.html

Subject classifications