Amina Abdurrahman: A formula for symplectic L-functions and Reidemeister torsion

Abstract:

We give a global cohomological formula for the central value of the L-function of a symplectic representation on a curve up to squares. The proof relies crucially on a similar formula for the Reidemeister torsion of 3-manifolds together with a symplectic local system. We sketch both analogous arithmetic and topological pictures. This is based on joint work with A. Venkatesh.