Sums of inverses in thin sets of finite fields
  We obtain lower bounds for the cardinality of $k$-fold sum-sets of reciprocals of elements of suitable defined short intervals in high degree extensions of finite fields. Combining our results with bounds for multilinear character sums we obtain new results on incomplete multilinear Kloosterman sums in finite fields. 
Igor E. Shparlinski and Ana Zumalac\'arregui
math.NT