There are two eminent still open conjectures for nonvanishing holomorphic Hardy functions f(z) on the unit disk. The Hummel–Scheinberg–Zalcman conjecture posed in 1977 extends Krzyz’s of 1968 to Hp spaces with finite p > 1 and states that Taylor’s coefficients f ? norm ?f?p ? sharply estimated by |cn| (2/e)1 ? 1/p, appropriate extremal functions. Both have been investigated many authors; howeve...