2019 Theses Doctoral

p-adic L-functions for non-critical adjoint L-values

Lee, Pak Hin

Let K be an imaginary quadratic field, with associated quadratic character α. We construct an analytic p-adic L-function interpolating the special values L(1, ad(f) ⊗ α) as f varies in a Hida family; these values are non-critical in the sense of Deligne.

Our approach is based on Greenberg--Stevens' idea of Λ-adic modular symbols. By considering cohomology with values in a space of p-adic measures, we construct a Λ-adic evaluation map that interpolates Hida's integral expression as the weight varies. The p-adic L-function is obtained by applying this map to a cohomology class corresponding to the given Hida family.