Witten zeta function at negative integersMPIM

by Kam Cheong Au (Universität zu Köln)

Wednesday Mar 5, 2025, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

"The Witten zeta function for a simple Lie algebra $\mathfrak{g}$ is defined by the Dirichlet series $$\mathfrak{g}(s) := \sum_{\rho} \frac{1}{(\dim \rho)^s},$$ where $\rho$ ranges over all irreducible representations of $\mathfrak{g}$. It has been popularized by Zagier to illustrate its special values at positive even integers.

Although not as nice as L-functions, it still satisfies several non-trivial properties with interesting consequence. In this talk, we prove a conjecture of Kurokawa and Ochiai which says $\mathfrak{g}(s)$ vanishes at negative even integers, we also mention a connection to some non-trivial identities about Riemann zeta values and Eisenstein series."

For lunch we will gather at 12:30 at the reception and go to pizzeria Tusculo Muensterblick.