小编Mat*_*vik的帖子

在J.Brian Conrey在图6中的论文"The Riemann Hypothesis"中,有一个素数定理中误差项的傅立叶变换图.请参见下图中左侧的图:

在由Chris King撰写的名为Primes out of Thin Air的博客文章中,有一个Matlab程序可以绘制频谱图.请参阅帖子开头右侧的情节.可以翻译成Mathematica:

数学:

 scale = 10^6;
 start = 1;
 fin = 50;
 its = 490;
 xres = 600;
 y = N[Accumulate[Table[MangoldtLambda[i], {i, 1, scale}]], 10];
 x = scale;
 a = 1;
 myspan = 800;
 xres = 4000;
 xx = N[Range[a, myspan, (myspan - a)/(xres - 1)]];
 stpval = 10^4;
 F = Range[1, xres]*0;

For[t = 1, t <= xres, t++,
 For[yy=0, yy<=Log[x], yy+=1/stpval,
 F[[t]] =
 F[[t]] +
 Sin[t*myspan/xres*yy]*(y[[Floor[Exp[yy]]]] …