2025/12/02 by Suzuho Osonoe, Osonoe, Suzuho, Maki Nakasuji +1
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2512.02335
We define the Kloosterman sum for SL4 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 SL4-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.