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MatsGranvik

xi function zeros plot

Aug 1st, 2020 (edited)
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  1. (*start xi function*)cons = 10;
  2. ww = 400;
  3. div = 10;
  4. real = 1/2;
  5. Monitor[TableForm[zz = Table[Clear[t, b, n, k, nn, x];
  6. z = N[cons + w/div, 20];
  7. polynomial =
  8. Normal[Series[
  9. 1/2 (real + x + z*N[I, 20])*((real + x + z*N[I, 20]) - 1)*
  10. Pi^(-(real + x + z*N[I, 20])/
  11. 2) Gamma[(real + x + z*N[I, 20])/2]*
  12. Zeta[(real + x + z*N[I, 20])], {x, 0, 10}]];
  13. digits = 20;
  14. b = With[{nn = 20},
  15. CoefficientList[Series[1/polynomial, {x, 0, nn}], x]];
  16. nn = Length[b] - 1;
  17. x = z*I + N[b[[nn - 1]]/b[[nn]], digits], {w, 0, ww}]];, w]
  18. g1 = ListLinePlot[Flatten[Im[zz]], DataRange -> {cons, cons + ww/div}]
  19. g2 = ListLinePlot[Flatten[Re[zz]], DataRange -> {cons, cons + ww/div},
  20. PlotRange -> {-2, 2}]
  21. zz
  22. (*end*)
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