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Canonical partition functions and Lee-Yang zeros of QCD at finite density andhigh temperature are studied. Recent lattice simulations have confirmed thatthe free energy of QCD is a quartic function of quark chemical potential attemperature slightly above pseudo-critical temperature $T_c$, as in the casewith a gas of free massless fermions.  We present analytic derivation of the canonical partition functions andLee-Yang zeros for this type of free energy using the saddle pointapproximation. We also perform lattice QCD simulation in a canonical approachusing the fugacity expansion of the fermion determinant, and carefully examineits reliability. By comparing the analytic and numerical results, we concludethat the canonical partition functions follow the Gaussian distribution of thebaryon number, and the accumulation of Lee-Yang zeros of these canonicalpartition functions exhibit the first-order Roberge-Weiss phase transition. Wediscuss the validity and applicable range of the result and its implicationsboth for theoretical and experimental studies.

Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition