English

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

Number Theory 2023-03-24 v1 Algebraic Topology

Abstract

We propose (and prove under some restrictions) that the square class of the central value of the LL-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 33-manifolds.

Keywords

Cite

@article{arxiv.2303.13436,
  title  = {Symplectic $L$-functions and symplectic Reidemeister torsion (mod squares)},
  author = {Amina Abdurrahman and Akshay Venkatesh},
  journal= {arXiv preprint arXiv:2303.13436},
  year   = {2023}
}