Prof. Dr. Johannes Sprang (Universität Duisburg-Essen)

Euler’s beautiful formula for the values of the Riemann zeta function at the positive even integers can be seen as the starting point of the investigation of special values of L-functions.
In particular, Euler’s result shows that all critical zeta values are rational up to multiplication with a particular period, here the period is a power of 2πi. Conjecturally this is expected to hold for all critical L-values of motives. In this talk, I will explain a joint result with Guido Kings on the algebraicity of critical Hecke L-values up to explicit periods for totally imaginary fields. As an application, I will discuss the construction of p-adic L-functions for such fields.