Publications [#352548] of Lillian B. Pierce

Papers Published

1. Pierce, LB; Xu, J, Burgess bounds for short character sums evaluated at forms, Algebra and Number Theory, vol. 14 no. 7 (January, 2020), pp. 1911-1951 [doi]
   (last updated on 2025/04/03)

   Abstract:
   We establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to a very general class of “admissible” forms. This n-dimensional Burgess bound is nontrivial for sums over boxes of sidelength at least qβ, with β > 1/2 − 1/(2(n + 1)). This is the first Burgess bound that applies in all dimensions to generic forms of arbitrary degree. Our approach capitalizes on a recent stratification result for complete multiplicative character sums evaluated at rational functions, due to the second author.