Skip to main content

Resurgence with quasi-modularity: outperforming Ramanujan

Posted in
Speaker: 
David Broadhurst
Affiliation: 
Open University, UK
Date: 
Wed, 14/08/2024 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

I describe recent progress on two intriguing problems. The first concerns improvements on Ramuajan's evaluation of odd zeta values, by expansion in $\exp (-2 \pi) < 1/535$. The second concerns a study of resurgence in the asymptotic expansion of Lambert series, where easily computable perturbative terms are accompanied by non-perturbative corrections in $\exp (-1/x)$ at small $x$. I shall explain how the pioneering work of Spencer Bloch, Pierre Vanhove and Matt Kerr, on elliptic polylogarithms from Feynman integrals, led to progress on both problems, by exploiting quasi-modularity.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A