Deligne’s conjecture for special values of Hecke L-functions states roughly that the critical L-values divided by certain periods are algebraic numbers. If one knows moreover integrality of these values one can try to construct p-adic L-functions. For Hecke characters over CM fields and ordinary p these are known results by Shimura, Blasius and Katz. In recent joint work with Sprang, we generalized these results to critical Hecke L-values over arbitrary fields. Using a new p-adic Fourier theory, which generalizes earlier results by Schneider and Teitelbaum, we can also construct for the first time a p-adic L-function for arbitrary prime numbers p. This was known so far only for Hecke characters over imaginary quadratic fields, by work of Katz and Boxall. In this talk I will explain these results and some of the ideas going into its proof.
Algebraicity of Hecke L-values and p-adic interpolation
13.01.2026 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: