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MatsGranvik

10 to power 7 Riemann zeta zero.

Jul 13th, 2021
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  1. (*Mathematica start*)Clear[f, s, n];
  2. nn = 7;(*10^15 zeta zero*)f[x_] := Zeta[x];
  3. (*The Franca-LeClair approximation of the zeta zeros:*)
  4. n = 140;(*increase "n" for better precision*)s =
  5. 1/2 + I*Table[
  6. 2*Pi*Exp[1]*Exp[ProductLog[(10^n - N[11/8, 80])/Exp[1]]], {n, nn,
  7. nn}];
  8. (*Root function for almost any function:*)
  9. Monitor[z =
  10. Table[s[[j]] +
  11. 1/(1 - Sum[((-1)^(k - 1)*Binomial[n - 1, k - 1])/
  12. f[k/n + s[[j]] - 1/n], {k, 1, n}]/
  13. Sum[((-1)^(k - 1)*Binomial[n - 1, k - 1])/f[k/n + s[[j]]], {k,
  14. 1, n}]), {j, 1, 1}], j]
  15. Zeta[z]
  16. (*end*)
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