  Canonical partition functions and Lee-Yang zeros of QCD at finite density and
high temperature are studied. Recent lattice simulations have confirmed that
the free energy of QCD is a quartic function of quark chemical potential at
temperature slightly above pseudo-critical temperature $T_c$, as in the case
with a gas of free massless fermions.
  We present analytic derivation of the canonical partition functions and
Lee-Yang zeros for this type of free energy using the saddle point
approximation. We also perform lattice QCD simulation in a canonical approach
using the fugacity expansion of the fermion determinant, and carefully examine
its reliability. By comparing the analytic and numerical results, we conclude
that the canonical partition functions follow the Gaussian distribution of the
baryon number, and the accumulation of Lee-Yang zeros of these canonical
partition functions exhibit the first-order Roberge-Weiss phase transition. We
discuss the validity and applicable range of the result and its implications
both for theoretical and experimental studies.
