Katz and Sarnak predicted that the one level density of the zeros
of a family of $L$-functions would fall into one of five categories.
In this paper, we show that the one level density for $L$-functions
attached to cubic Galois number fields falls into the category
associated with unitary matrices.
L-function, one level density
11M06 - $\zeta (s)$ and $L(s, \chi)$
11M26 - Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11M50 - Relations with random matrices