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Theorems reveal the Sato–Tate distribution of Kloosterman sums in function fields, indicating significant implications for local systems.
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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Fu et al. (2025) studied this question.
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