## Geometry Seminar - Abstracts

### Talk

Tuesday 10 May 2022, 16:00 - 17:00 in HG03.054

**Johannes Sprang** (Duisburg-Essen)

*Algebraicity of critical Hecke L-values*

### Abstract

In 1735, Euler discovered his well-known formula for the values of the Riemann zeta function at the positive even integers. In particular, Euler's result shows that all these 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, we will focus on L-functions of number fields. In the first part of the talk, we will discuss the 'critical' and 'non-critical' L-values exemplary for the Riemann zeta function. Afterwards, we will head on to more general number fields and explain a joint result with Guido Kings on the algebraicity of critical Hecke L-values for totally imaginary fields up to explicit periods.

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