Equidistribution of Kloosterman Sums Over Function Fields
Abstract We prove the Sato–Tate distribution of Kloosterman sums over function fields with explicit error terms, when the places vary in arithmetic progressions or short intervals. A joint Sato–Tate distribution of finitely many Kloosterman sums is also proved. The arguments in this paper also apply to local systems with $\textrm{SL}(2)$ monodromy and suitable ramification restrictions.
Authors
- Yuk-Kam Lau (ORCID: https://orcid.org/0000-0003-2765-5392)
- Wen-Ching Winnie Li
- Ping Xi
- Lei Fu (ORCID: https://orcid.org/0000-0002-5536-0842)
Institutions
- Pennsylvania State University (US)
- Weihai Municipal Hospital (CN)
- Weihai Science and Technology Bureau (CN)
- Xi'an Jiaotong University (CN)
- University of Hong Kong (HK)
- Tsinghua University (CN)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-07-14
- DOI
- https://doi.org/10.1093/imrn/rnaf229
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Simons Foundation
- Glaucoma Research Foundation
- National Natural Science Foundation of China