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.
|Number of pages
|Illinois Journal of Mathematics
|Published - Sept 2002