Zeta Zeros Spacing Tests

SetDirectory["D:/GEOMETRY/INFOGEOM/QuantumInformation"]

<<HypothesisTesting`
Needs["BarCharts`"]

B=ReadList["ZetaZeros1.txt",Number];

Length[B]

Clear[SZ]

SZ=Table[(B[[k+1]]-B[[k]])/0.749074,{k,1,Length[B]-1}];

Example: Statistics of spacings of integer 1 :-{Mean,SD,Gamma}

{Mean[SZ//Evaluate],(Sqrt[Variance[SZ//Evaluate]]),(((Mean[SZ//Evaluate])^2)/(Variance[SZ//Evaluate]))}//N

BinCounts[SZ,{0,7,0.1}]

70 Mean[BinCounts[SZ,{0,7,0.1}]]//N

zer=BarChart[BinCounts[SZ,{0,3,0.1}],GridLines->Automatic,Frame->True]

gam=ListPlot[100000Table[(∫_(k 0.1)^((k+1)0.1)) (((5.427^5.427) (E^(-x 5.427)) (x^4.427))/(  Gamma[5.427]))\[DifferentialD]x,{k,0,30}],PlotStyle->{RGBColor[1,0,0],AbsolutePointSize[7]},GridLines->Automatic,Frame->True]

Show[zer,gam]

Gamma parameter is expected to be 3 for GUE according to Berry, which zeta zeros is expected to follow according to Rudnick

Plot[{(((5.427^5.427) (E^(-x 5.427)) (x^4.427))/(Gamma[5.427])),(((3^3) (E^(-x 3)) (x^2))/(Gamma[3]))},{x,0,3}]