Burgess bounds for short character sums evaluated at forms
Publication
, Journal Article
Pierce, LB; Xu, J
Published in: Algebra and Number Theory
January 1, 2020
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.
Duke Scholars
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Published In
Algebra and Number Theory
DOI
ISSN
1937-0652
Publication Date
January 1, 2020
Volume
14
Issue
7
Start / End Page
1911 / 1951
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
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ICMJE
MLA
NLM
Pierce, L. B., & Xu, J. (2020). Burgess bounds for short character sums evaluated at forms. Algebra and Number Theory, 14(7), 1911–1951. https://doi.org/10.2140/ant.2020.14.1911
Pierce, L. B., and J. Xu. “Burgess bounds for short character sums evaluated at forms.” Algebra and Number Theory 14, no. 7 (January 1, 2020): 1911–51. https://doi.org/10.2140/ant.2020.14.1911.
Pierce LB, Xu J. Burgess bounds for short character sums evaluated at forms. Algebra and Number Theory. 2020 Jan 1;14(7):1911–51.
Pierce, L. B., and J. Xu. “Burgess bounds for short character sums evaluated at forms.” Algebra and Number Theory, vol. 14, no. 7, Jan. 2020, pp. 1911–51. Scopus, doi:10.2140/ant.2020.14.1911.
Pierce LB, Xu J. Burgess bounds for short character sums evaluated at forms. Algebra and Number Theory. 2020 Jan 1;14(7):1911–1951.
Published In
Algebra and Number Theory
DOI
ISSN
1937-0652
Publication Date
January 1, 2020
Volume
14
Issue
7
Start / End Page
1911 / 1951
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics