Hyperbolic geodesics, Krzyz's conjecture and beyond

Samuel L. Krushkal

In 1968, Krzyz conjectured that for non-vanishing holomorphic functions $f(z)=c_0+c_{1}z+\dots$ in the unit disk with $|f(z)|\le 1$, we have the sharp bound $|c_n|\le 2/e$…