Number Theory Seminar
p-adic L-functions for totally imaginary fields
Speaker: Johannes Sprang (Universität Duisburg-Essen)Date: Tuesday, 24 February 2026 - 14:30Place: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
The p-adic L-function of Kubota and Leopoldt p-adically interpolates the values of the Riemann zeta function at negative integers. More generally, for other L-functions one may ask for a p-adic L-function, which is typically characterized by the interpolation of certain critical L-values up to explicit periods.
In the case of Hecke L-functions, it is known that critical values can exist only when the underlying number field is either totally real or totally imaginary. For totally real number fields, p-adic L-functions are well understood. The totally imaginary case is substantially more difficult. In particular, for non-ordinary primes, such p-adic L-functions for totally imaginary number fields beyond the quadratic case have so far been unknown.
In this talk, I will explain joint work in progress with Guido Kings about the construction of such p-adic L-functions for totally imaginary fields.
