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- (*Mathematica start*)Clear[f, s, n];
- nn = 7;(*10^15 zeta zero*)f[x_] := Zeta[x];
- (*The Franca-LeClair approximation of the zeta zeros:*)
- n = 140;(*increase "n" for better precision*)s =
- 1/2 + I*Table[
- 2*Pi*Exp[1]*Exp[ProductLog[(10^n - N[11/8, 80])/Exp[1]]], {n, nn,
- nn}];
- (*Root function for almost any function:*)
- Monitor[z =
- Table[s[[j]] +
- 1/(1 - Sum[((-1)^(k - 1)*Binomial[n - 1, k - 1])/
- f[k/n + s[[j]] - 1/n], {k, 1, n}]/
- Sum[((-1)^(k - 1)*Binomial[n - 1, k - 1])/f[k/n + s[[j]]], {k,
- 1, n}]), {j, 1, 1}], j]
- Zeta[z]
- (*end*)
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