Multiple zeta star values, limits, and pi-power identitiesMPIM

by Steven Charlton (Universität zu Köln)

Tuesday Apr 28, 2026, 2:00 PM → 3:00 PM Europe/Berlin

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

PLeaSANT

Multiple zeta (star) values are a multivariable generalisation of Riemann zeta values like $\zeta(2)=\pi^2/6$ and $\zeta(3)$; their arithmetic nature (irrational or transcendental) is still largely conjectural.  They play a rather important role in high-energy physics calculations, acting as a bridge between number theory and particle physics.  One of the main goals is to understand their algebraic structure, and all of the relations and identities they satisfy.

 

I'll discuss some on-going work with Danylo Radchenko, on the limit behaviour of multiple zeta star values, and the applications to understanding some special evaluations, new and old.  The motivation comes from a strange conjectural identity for a weight $8n+4$ multiple zeta star value as a multiple of $\pi^{8n+4}$, and its possible generalisations.