Thursday, December 28, 2017

Furthermore............fractals................................14.13 i.............the location of the 1st zero.............



RiemannZetaAbsThe above plot shows |zeta(1/2+it)| for t between 0 and 60. As can be seen, the first few nontrivial zeros occur at the values given in the following table (Wagon 1991, pp. 361-362 and 367-368; Havil 2003, p. 196; Odlyzko), where the corresponding negative values are also roots. The integers closest to these values are 14, 21, 25, 30, 33, 38, 41, 43, 48, 50, ... (OEIS A002410). The numbers of nontrivial zeros less than 10, 10^2, 10^3, ... are 0, 29, 649, 10142, 138069, 1747146, ... (OEIS A072080; Odlyzko).
nSloanet_n
1A05830314.134725
221.022040
325.010858
430.424876
532.935062
637.586178

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