Monday, March 26, 2018

2pi.................is also a 2 and a 3................just like the primes start out............I mentioned that before................2 and 3...........how e and pi starts out..................the square root of 13.........starts out.....3.60............like full circle................2 pi.............6.28..................6 + 28 = 34..............kinda like pi..................one number ............and 3 and 4.........separated by single digits and double digits...............fusing together..........separating.........atomic fusion and fission................



RiemannZetaZerosContoursReIm
The position of the complex zeros can be seen slightly more easily by plotting the contours of zero real (red) and imaginary (blue) parts, as illustrated above. The zeros (indicated as black dots) occur where the curves intersect.
RiemannZetaSurfaces
The figures above highlight the zeros in the complex plane by plotting |zeta(z)| (where the zeros are dips) and 1/|zeta(z)| (where the zeros are peaks).
RiemannZetaAbs
The 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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