when they exploit the relationship by Berry and Keating between the Riemann zeros and eigenvalues of random matrices
why do they choose $$ \frac{\gamma _{n}}{2\pi}log \frac{\gamma}{2\pi e} $$ as a Random variable
however why are they ignoring the number $ \frac{1}{\pi}arg \zeta (1/2+is) $
i am referring to the paper
http://www.maths.bris.ac.uk/~majpk/papers/67.pdf
why he just ignore the scillating term proportional to the argument of the zeta function of the critical lines.
The normalization of zeros is chosen to make the number of zeta zeros with imaginary part in the interval $[0,W]$ behave like $W$ plus lower order terms, so that upon dividing by $W$ and taking the limit, you get a density function on the upper critical line. Why are you concerned about the argument of zeta?
The point is that if we now look at pair correlations of how far apart any given pair of zeros ought to be, then this behaves in a very similar way to the pair-correlations in random unitary matrices.