New power-saving bounds are proven for all generalized Kloosterman sums on GL_n, using explicit parametrizations and the Weil bound.
Kloosterman sums on orthogonal groups
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abstract
We study Kloosterman sums on the orthogonal groups $SO_{3,3}$ and $SO_{4,2}$, 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.
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2024 1verdicts
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Bounds for Kloosterman Sums for $\mathrm{GL}_n$
New power-saving bounds are proven for all generalized Kloosterman sums on GL_n, using explicit parametrizations and the Weil bound.