Kloosterman sums on orthogonal groups

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2025年6月23日

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Catinca Mujdei

摘要

We study Kloosterman sums on the orthogonal groups $SO_{3,3}$ $S O_{3, 3}$ and $SO_{4,2}$ $S O_{4, 2}$ , associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and p-adic analysis.