Does anyone know what the asymptotic of the differences between successive zeta zeros is?

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It appears that $\zeta(n)$ is not a bad asymptotic, when the data range is stretched:

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r = 3000; Show[ListPlot[(Differences[Table[Im[N[ZetaZero[n]]],{n, 1, r}]]), 
m = 100; ListLinePlot[Table[Zeta[n], {n, 0, Log[r], 0.01}], 
DataRange -> {-r/\[Pi], r}, PlotStyle -> Red]]

(as is $\pi/\log\log\gamma_n$ following on from the link suggested by barto). I don't know how to write this mathematically though.

  • 3
    $\begingroup$ Related: this and this linked question on MO. $\endgroup$ – punctured dusk Jun 3 '14 at 19:57
  • $\begingroup$ The best possible asymptotic to the Riemann zeta zeros, as pointed out by reuns, is the functional inverse of the Riemann Siegel theta function. As a Mathematica program that would be: Round[Table[ N[InverseFunction[RiemannSiegelTheta][Pi*(n - 1/2)], 30], {n, 0, 12}]] $\endgroup$ – Mats Granvik Oct 12 '18 at 14:53

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