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Burgess bounds for short character sums evaluated at forms II: the mixed case

Publication ,  Journal Article
Pierce, LB
2020

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.

Duke Scholars

Publication Date

2020
 

Publication Date

2020