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arXiv · 2303.13436

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

Amina Abdurrahman·Akshay Venkatesh
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Abstract

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.

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Amina Abdurrahman, Akshay Venkatesh. 2023-03-23. Symplectic $L$-functions and symplectic Reidemeister torsion (mod squares). https://arxiv.org/abs/2303.13436

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