Mixed character sums

I will talk about a distributional result for 'mixed character sums', which are exponential sums with multiplicative coefficients given by values of a Dirichlet character. As a deterministic application, we construct polynomials with $\pm 1$ coefficients with large Mahler measure, establishing a new record in Mahler's problem. This is joint work with Jonathan W. Bober and Oleksiy Klurman.