Publications [#356103] of Lillian B. Pierce

Papers Published

1. Pierce, LB, Burgess bounds for short character sums evaluated at forms II: the mixed case, vol. 12 no. 1 (2020), pp. 151-179
   (last updated on 2025/04/03)

   Abstract:
   This work proves a Burgess bound for short mixed character sums in $n$ dimensions. The non-principal multiplicative character of prime conductor $q$ may be evaluated at any "admissible" form, and the additive character may be evaluated at any real-valued polynomial. The resulting upper bound for the mixed character sum is nontrivial when the length of the sum is at least $q^{\beta}$ with $\beta> 1/2 - 1/(2(n+1))$ in each coordinate. This work capitalizes on the recent stratification of multiplicative character sums due to Xu, and the resolution of the Vinogradov Mean Value Theorem in arbitrary dimensions.