2019 Theses Doctoral

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

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.

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## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Urban, Eric Jean-Paul
- Degree
- Ph.D., Columbia University
- Published Here
- November 6, 2019