  We address several aspects of lattice QCD calculations of the hadronic vacuum
polarization and the associated Adler function. We implement a representation
derived previously which allows one to access these phenomenologically
important functions for a continuous set of virtualities, irrespective of the
flavor structure of the current. Secondly we present a theoretical analysis of
the finite-size effects on our particular representation of the Adler function,
based on the operator product expansion at large momenta and on the spectral
representation of the Euclidean correlator at small momenta. Finally, an
analysis of the flavor structure of the electromagnetic current correlator is
performed, where a recent theoretical estimate of the Wick-disconnected diagram
contributions is rederived independently and confirmed.
