Symplectic L-functions and symplectic Reidemeister torsion (mod squares)

• 成果类型: Article
• 署名作者: Abdurrahman, Amina; Venkatesh, Akshay
• 署名单位: Princeton University; Institute for Advanced Study - USA
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01349-6
• 发表日期: 2025
• 页码: 717-839
• 关键词: k-theory; FIELDS; Generators; conjecture; sheaves

摘要

We propose (and prove under some restrictions) that the square class of the central value of the L-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.