Equidistribution of Kloosterman Sums Over Function Fields

Lei Fu; Yuk Kam Lau; Wen Ching Winnie Li; Ping Xi

doi:10.1093/imrn/rnaf229

Equidistribution of Kloosterman Sums Over Function Fields

Lei Fu, Yuk Kam Lau, Wen Ching Winnie Li, Ping Xi

Mathematics

Research output: Contribution to journal › Article › peer-review

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 SL(2) monodromy and suitable ramification restrictions.

Original language	English (US)
Article number	rnaf229
Journal	International Mathematics Research Notices
Volume	2025
Issue number	15
DOIs	https://doi.org/10.1093/imrn/rnaf229
State	Published - Aug 1 2025

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnaf229

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title = "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 SL(2) monodromy and suitable ramification restrictions.",

author = "Lei Fu and Lau, \{Yuk Kam\} and Li, \{Wen Ching Winnie\} and Ping Xi",

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N2 - 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 SL(2) monodromy and suitable ramification restrictions.

AB - 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 SL(2) monodromy and suitable ramification restrictions.

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DO - 10.1093/imrn/rnaf229

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Equidistribution of Kloosterman Sums Over Function Fields

Abstract

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