  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 $p \ge
2$.
