The so called GUE hypothesis (see e.g. [1]) states that, in a certain limit, the zeros of the Riemann zeta function on the critical line Re have the same joint distribution as that of the eigenvalues of a random matrix from the Gaussian Unitary Ensemble (GUE) of large (formally infinite) dimensional random Hermitian matrices. Denoting the zeros by , where n labels the zeros sequentially along the critical line, the GUE hypothesis applies in the limit , with each scaled by the mean density of zeros at , so that the mean spacing between zeros is unity (any finite value will do).
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