Math @ Duke

Publications [#352548] of Lillian B. Pierce
Papers Published
 Pierce, LB; Xu, J, Burgess bounds for short character sums evaluated at forms,
Algebra & Number Theory, vol. 14 no. 7
(January, 2020),
pp. 19111951 [doi]
(last updated on 2021/04/20)
Abstract: © 2020, Mathematical Sciences Publishers. All rights reserved. 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 ndimensional 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.


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