The Hörmander-Bernhardsson extremal function

We pin down the function $\phi$ of minimal $L^1$ norm among all functions $f$
of exponential type at most $\pi$ for which $f(0)=1$. The problem of describing
$\phi$ has surfaced in many different contexts during the past 35 years, including
analytic number theory and the study of prime gaps. Our work is inspired by a
remarkable 1993 paper of Hörmander and Bernhardsson. The talk is based on joint
work with Andriy Bondarenko, Joaquim Ortega-Cerdá, and Danylo Radchenko.