Parametrization of Kloosterman sets and $\mathrm{SL}_3$-Kloosterman sums

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ID: 283366
2020
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Abstract
We stratify the $\mathrm{SL}_3$ big cell Kloosterman sets using the reduced word decomposition of the Weyl group element, inspired by the Bott-Samelson factorization. Thus the $\mathrm{SL}_3$ long word Kloosterman sum is decomposed into finer parts, and we write it as a finite sum of a product of two classical Kloosterman sums. The fine Kloosterman sums end up being the correct pieces to consider in the Bruggeman-Kuznetsov trace formula on the congruence subgroup $\Gamma_0(N)\subseteq \mathrm{SL}_3(\mathbb{Z})$. Another application is a new explicit formula, expressing the triple divisor sum function in terms of a double Dirichlet series of exponential sums, generalizing Ramanujan's formula.
Reference Key
nakasuji2020parametrization Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Eren Mehmet Kıral; Maki Nakasuji
Journal arXiv
Year 2020
DOI
DOI not found
URL
http://arxiv.org/abs/2001.01936v1
Keywords
math.nt 11l05 (primary), and 11f22, 11f72 (secondary)

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