On the Erd\H{o}s-Falconer distance problem for two sets of different   size in vector spaces over finite fields
  We consider a finite fields version of the Erd\H{o}s-Falconer distance problem for two different sets. In a certain range for the sizes of the two sets we obtain results of the conjectured order of magnitude. 
Rainer Dietmann
math.NT math.CO