# Burgess bounds for short character sums evaluated at forms

@article{Pierce2020BurgessBF, title={Burgess bounds for short character sums evaluated at forms}, author={L. Pierce and J. Xu}, journal={Algebra & Number Theory}, year={2020}, volume={14}, pages={1911-1951} }

In this work 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 $q^{\beta}$, with $\beta > 1/2 - 1/(2(n+1))$. This is the first Burgess bound that applies in all dimensions to generic forms of arbitrary degree. Our approach capitalizes on a… CONTINUE READING

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