Thursday, March 1, 2018

All that illustrates several imp. numbers/processes, etc..........at once..........overlap for one.........hidden dimensions...............................unfolding.....................14.13i..........14 + 13 = 27...........like e.............without the dec point..............of course adding it like that.........is through a dec point...........and pi....................14.13.............beg to middle........is 14...............end to beg........is 31......overlap the ones..........31 14........it is pi.........314...............pi and e at once........if u add the 1st 3 numbers of e and pi................2.71 + 3.14................= 5.85..........two golden ratios and two 13s.............taken from the middle number............8.................8/5 = 1.6...........8/5 = 1.6...........1.6 + 1.6 = 3.2..................like 2, 3 the start of all primes......but inverted.........5 + 8 = 13..............8 + 5 = 13......................13 + 13 = 26...............1st 25 primes..........words into math (like mathematical logic)............1 + 25 = 26...................


RiemannZetaSurfacesThe 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).
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
XiFunctionRootsThe so-called xi-function xi(z) defined by Riemann has precisely the same zeros as the nontrivial zeros of zeta(z) with the additional benefit that xi(z) is entire and xi(1/2+it) is purely real and so are

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