Character sums with Beatty sequences on Burgess-type intervals
  We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence $\{[\alpha n + \beta] : n =1,2,... \}$, where $\alpha,\beta\in\R$, and $\alpha$ is irrational. Our bounds are nontrivial over the same short intervals for which the classical character sum estimates of Burgess have been established. 
William D. Banks and Igor E. Shparlinski