$SL_4$-Kloosterman sum via the Bruhat decomposition
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908686960558080 |
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| author | Osonoe, Suzuho Nakasuji, Maki |
| author_facet | Osonoe, Suzuho Nakasuji, Maki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $SL_4$-Kloosterman sum via the Bruhat decomposition Osonoe, Suzuho Nakasuji, Maki Number Theory 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. |
| title | $SL_4$-Kloosterman sum via the Bruhat decomposition |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.02335 |