Gram's Law

Author

Eric W. Weisstein
January 2, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/GramsLaw.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GramsLaw.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Plot

<<Utilities`Plot`

There are precisely $n+1$ zeros of $Z(t)$ between 0 and $g_n$ (Edwards 2001, p. 171).

PlotRoots[RiemannSiegelZ[t],{t,0,50},PlotStyle->{Red,PointSize[.01]},
AxesLabel->TraditionalForm/@{t,RiemannSiegelZ[t]},
Epilog->{{Blue,PointSize[.03],{Point[{#,0}],Line[{{#,-10},{#,10}}]}&/@GramPoint/@Range[0,10]}}]