  We study the Fourier coefficients b(k,T) of the net baryon number density in
strongly interacting matter at finite temperature. We show that singularities
in the complex chemical potential plane connected with phase transitions are
reflected in the asymptotic behavior of the coefficients at large k. We derive
the scaling properties of b(k,T) near a second order phase transition in the
O(4) and Z(2) universality classes. The impact of first order and crossover
transitions is also examined. The scaling properties of b(k,T) are linked to
the QCD phase diagram in the temperature and complex chemical potential plane.
