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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