MatsGranvik

Möbius function from itself at s equal infinity

Jan 24th, 2022
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  1. (*start*)
  2. Clear[nn, s, c, z, x];
  3. nn = 16;
  4. s = 10000;
  5. c = 10000;
  6. z = 10000;
  7. x = 10000;
  8.  
  9. (*Table[Limit[Zeta[ss] \
  10. Total[1/Divisors[n]^(ss-z-x)*MoebiusMu[Divisors[n]]]/n^c,ss->s],{n,1,\
  11. nn}];*)
  12.  
  13. A = Table[
  14. Table[If[Mod[n, k] == 0, MoebiusMu[k]*k^z/n^s, 0], {k, 1, nn}], {n,
  15. 1, nn}];
  16. B = Table[
  17. Table[If[Mod[k, n] == 0, n^x/k^c, 0], {k, 1, nn}], {n, 1, nn}];
  18.  
  19. TableForm[T = Chop[N[A.B]]]
  20.  
  21. "Double sum:"
  22. Sum[Sum[N[T, 20][[n, k]], {k, 1, nn}], {n, 1, nn}]
  23.  
  24. "Generating function for the double sum:"
  25. N[Zeta[s]*Zeta[c]/Zeta[s + c - z - x], 20]
  26. (*end*)
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