Advertisement
Not a member of Pastebin yet?
Sign Up,
it unlocks many cool features!
- (*Mathematica 8 start*)
- Clear[s, z, c, nn, n, k, kk]
- z = N[ZetaZero[1], 20];
- c = N[ZetaZero[1], 20];
- nn = 64;
- A = Table[
- Table[If[Mod[n, k] == 0, Sqrt[k]/n^z, 0], {k, 1, nn}], {n, 1,
- nn}]; B =
- Table[Table[
- If[Mod[k, n] == 0, MoebiusMu[n]*Sqrt[n]/k^c, 0], {k, 1, nn}], {n,
- 1, nn}];
- Print["Matrix sum"]
- N[Total[Total[A.B]], 20]
- Print["Half analytic continuation"]
- N[Sum[Limit[
- Zeta[s] Total[1/Divisors[n]^(s - 1)*MoebiusMu[Divisors[n]]],
- s -> z]/n^c, {n, 1, nn}], 20]
- Print["Complete analytic continuation"]
- N[Zeta[z]*Zeta[c]/Zeta[c + z - 1], 20]
- Clear[c, ss, t]
- ss = 100;
- c = 1 + 1/ss;
- sigma = 1/2;
- Print["Plot of matrix sum on the critical line"]
- A = Table[
- Table[If[Mod[n, k] == 0, Sqrt[k]/n^(sigma + I*t), 0], {k, 1,
- nn}], {n, 1, nn}]; B =
- Table[Table[
- If[Mod[k, n] == 0, MoebiusMu[n]*Sqrt[n]/k^1, 0], {k, 1, nn}], {n,
- 1, nn}];
- Plot[Re[Total[Total[A.B]]], {t, 0, 60}]
- Print["Plot of half analytic continuation on the critical line"]
- Plot[Re[Sum[
- Zeta[sigma + I*t] Total[
- 1/Divisors[n]^(sigma + I*t - 1)*MoebiusMu[Divisors[n]]]/n^1, {n,
- 1, 30}]], {t, 0, 60}]
- Print["Plot of analytic continuation on the critical line"]
- Plot[Re[N[Zeta[sigma + I*t]*Zeta[c]/Zeta[c + sigma + I*t - 1],
- 20]], {t, 0, 60}, PlotRange -> {0, ss + 2}]
- (*Mathematica 8 end*)
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement