With the p.d.f. for the infinite GUE now evaluated, we can further test the GUE hypothesis by calculating for sequences of consecutive zeros of the Riemann zeta function, using the data of [1]. Three sets of consecutive zeros were analyzed, the data sets starting at zero number , and respectively. The quantity , where with denoting the smoothed local density of zeros at , was calculated and a histogram was constructed for the number of values out of the that were tested that fell into the intervals , . In Figure 2 the corresponding empirical values of at the points are plotted as a histogram and compared with the value of for the infinite GUE. The convergence towards the GUE value as the magnitude of the imaginary part increases is evident.
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