Character sums with Beatty sequences on Burgess-type intervals

Abstract

We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence $\{[\alpha n+\beta ]:n=1,2,...\}$, where $\alpha ,\beta \in \mathbb{R}$, 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.