  The Bielefeld Parma Collaboration has in recent years put forward a method to
probe finite density QCD by the detection of Lee-Yang singularities. The
location of the latter is obtained by multi-point Pad\`e approximants, which
are in turn calculated matching Taylor series results obtained from Monte Carlo
computations at (a variety of values of) imaginary baryonic chemical potential.
The method has been successfully applied to probe the Roberge Weiss phase
transition and preliminary, interesting results are showing up in the vicinity
of a possible QCD critical endpoint candidate. In this talk we will be
concerned with a couple of significant aspects in view of a more powerful
application of the method. First, we will discuss the possibility of detecting
finite size scaling of Lee-Yang/Fisher singularities in finite density
(lattice) QCD. Second, we will briefly mention our attempts at detecting both
singularities in the complex chemical potential plane and singularities in the
complex temperature plane. The former are obtained from rational approximations
which are functions of the chemical potential at given values of the
temperature; the latter are obtained from rational approximations which are
functions of the temperature at given values of the chemical potential.
