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arXiv · 2512.02335

$SL_4$-Kloosterman sum via the Bruhat decomposition

Suzuho Osonoe·Maki Nakasuji
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Abstract

We define the Kloosterman sum for $SL_4$ over the Kloosterman set via the Bruhat decomposition and stratify the Kloosterman set using the reduced word decomposition of the Weyl group element. The Kloosterman sum for an $SL_4$-long word is decomposed into finer parts (called the fine Kloosterman sum), and can be written as a finite sum of a product of two classical Kloosterman sums.

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Suzuho Osonoe, Maki Nakasuji. 2025-12-02. $SL_4$-Kloosterman sum via the Bruhat decomposition. https://arxiv.org/abs/2512.02335

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