Connections Between Special Values of L-Functions and Scattering Amplitudes

Watch a 52-minute conference talk from the Arithmetic Quantum Field Theory Conference where Kim Klinger-Logan from Kansas State University explores the fascinating connections between L-functions' zeros and special values and scattering amplitudes. Delve into differential equations of the form $(\Delta-\lambda)f = S$ on $X=SL(2,\Z)\SL(2,\R)/SO(2,\R)$ where $\Delta=y^2(\partial_x^2+\partial_y^2)$ and $H^{-\infty}(X)\cup M$, examining how these equations bridge number theory and physics. Learn about the groundbreaking work by Bombieri and Garrett linking eigenvalue solutions to L-function zeros, while also understanding how physicists like Green, Russo, and Vanhove connected similar eigenfunction solutions to 4-graviton scattering amplitude coefficients. Discover recent developments in finding solutions to these equations through collaborative research with Ksenia Fedosova, Stephen D. Miller, Danylo Radchenko and Don Zagier.