Advertisement
MatsGranvik

Mobius function times n approximately as eigenvalues

Aug 2nd, 2013
876
0
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 1.06 KB | None | 0 0
  1. (*Mathematica 8 program start*)
  2. (*The Mobius function times "n" approximately as the eigenvalues of a matrix*)
  3. Clear[nn, n, k, d, kolumn]
  4. a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]]
  5. Do[nn = j;
  6. A3 = Range[nn]*0;
  7. Do[kolumn = i;
  8. A1 = Table[Table[a[GCD[n, k]], {k, 1, nn}], {n, 1, nn}];
  9. MatrixForm[A1];
  10. A1[[All, kolumn]];
  11. MatrixForm[
  12. Table[Table[
  13. If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
  14. 0], {k, 1, nn}], {n, 1, nn}]];
  15. a1 = Table[
  16. Total[Table[
  17. If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
  18. 0], {k, 1, nn}]], {n, 1, nn}];
  19. a2 = Sign[a1]*Exp[Exp[Abs[a1]]];
  20. A2 = Table[
  21. Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}], {n, 1, nn}];
  22. MatrixForm[A2];
  23. a3 = Table[
  24. Total[Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}]], {n,
  25. 1, nn}];
  26. A3[[i]] = a3;, {i, 1, nn}]
  27. MatrixForm[A3];
  28. (*Print[N[Log[Log[-Min[Eigenvalues[A3]]]],12]]*)
  29. Print[N[Sign[Eigenvalues[A3]] Log[Log[Abs[Eigenvalues[A3]]]],
  30. 12]], {j, 1, 13}]
  31. (*program end*)
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement