Title: One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions,
Abstract: In this paper, we prove some one level density results for the low-lying
zeros of famliies of quadratic and quartic Hecke $L$-functions of the Gaussian
field. As corollaries, we deduce that, respectively, at least $94.27 \%$ and
$5\%$ of the members of the quadratic family and the quartic family do not
vanish at the central point.