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.
The figures above highlight the zeros in the complex plane by plotting (where the zeros are dips) and (where the zeros are peaks). The above plot shows for 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, , , ... are 0, 29, 649, 10142, 138069, 1747146, ... (OEIS A072080; Odlyzko).
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Tuesday, March 6, 2018
Something else Lorenz wrote that seems imp. in what Riemann did.........for one things........BOTH are dynamical systems...........so they are similar..........so they tell me.....dynamical systems........................but rounding off..............truncating........what else does that tell u??............Lorenz said it................the rounded off numbers dominated...........but WHY? It might be b/c the 1st few are more imp than the others............1/2 + 14.13i.............and expanded is probably the most imp..............both 14 and 21..........are within the square root of 2................initial conditions........what comes 1st carries more weight.....................that is what that tells me......
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