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

Publication ,  Journal Article
Pierce, LB
Published in: Rivista di Matematica della Universita di Parma
January 1, 2021

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 qβwith β > 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

Published In

Rivista di Matematica della Universita di Parma

EISSN

2284-2578

ISSN

0035-6298

Publication Date

January 1, 2021

Volume

12

Issue

1

Start / End Page

151 / 179

Related Subject Headings

  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Pierce, L. B. (2021). Burgess bounds for short character sums evaluated at forms II: the mixed case. Rivista Di Matematica Della Universita Di Parma, 12(1), 151–179.
Pierce, L. B. “Burgess bounds for short character sums evaluated at forms II: the mixed case.” Rivista Di Matematica Della Universita Di Parma 12, no. 1 (January 1, 2021): 151–79.
Pierce LB. Burgess bounds for short character sums evaluated at forms II: the mixed case. Rivista di Matematica della Universita di Parma. 2021 Jan 1;12(1):151–79.
Pierce, L. B. “Burgess bounds for short character sums evaluated at forms II: the mixed case.” Rivista Di Matematica Della Universita Di Parma, vol. 12, no. 1, Jan. 2021, pp. 151–79.
Pierce LB. Burgess bounds for short character sums evaluated at forms II: the mixed case. Rivista di Matematica della Universita di Parma. 2021 Jan 1;12(1):151–179.

Published In

Rivista di Matematica della Universita di Parma

EISSN

2284-2578

ISSN

0035-6298

Publication Date

January 1, 2021

Volume

12

Issue

1

Start / End Page

151 / 179

Related Subject Headings

  • 4904 Pure mathematics
  • 0101 Pure Mathematics