Quasiconformal deformations of nonvanishing $H^p$ functions and the Hummel-Scheinberg-Zalcman conjecture

Recently the author proved that the 1977 Hummel-Scheinberg-Zalcman conjecture on coefficients of nonvanishing $H^p$ functions is true for all $p=2m,m\in \mathbb{N}$, i.e., for the Hilbertian Hardy spaces $H^{2m}$. As a consequence, this also implies a proof of the Krzyz conjecture for bounded nonvanishing functions which originated this direction. In the present paper, we solve the problem for all spaces $H^p$ with $p\ge 2$.