A Dirichlet series coefficient approach to the Riemann hypothesis

Mathematica 8


Clear[t, A];
nn = 12;
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
t[n, k] =
If[n 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
A = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
A[[1, All]] = 0;
Print["A accumulated"]
MatrixForm[A];
MatrixForm[Accumulate[A]]
Print["B"]
B = Table[Table[If[Mod[n, k] == 0, 1 - k, 1], {n, 1, nn}], {k, 1, nn}];
MatrixForm[B];
DD = Table[
MatrixExp[
1/2*Table[
Table[If[Mod[n, k] == 0, B[[i]][[n/k]], 0], {k, 1, nn}], {n, 1,
nn}]][[All, 1]], {i, 1, nn}];
MatrixForm[DD]

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