A note on the multiplicative structure of an additively shifted product   set, AA+1
  We consider the multiplicative structure of sets of the form AA+1, where where A is a large, finite set of real numbers. In particular, we show that the additively shifted product set, AA+1 must have a large part outside of any generalized geometric progression of comparable length. We prove an analogous result in finite fields as well. 
Steven Senger
math.CO math.NT