## Character Sums over Integers with Restricted g-ary Digits

##### Abstract

We establish upper bounds for multiplicative character sums and exponential sums over sets of integers that are described by various
properties of their digits in a fixed base g ≥ 2. Our main tools are the Weil and Vinogradov bounds for character sums and exponential
sums. Our results can be applied to study the distribution of quadratic non-residues and primitive roots among these sets of integers.