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Statement

Notation (p. 125): $E$ is the set where $|f|<1$ and $D_r$ the open disk $|z|<r$.

Problem 7 (p. 142). "If all the zeros of $f$ lie in $D_r$ $(r<2)$, does the set $E$ have a component with diameter greater than $2-r$?"

Source. P. Erdős, F. Herzog, G. Piranian, Metric properties of polynomials, J. Analyse Math. 6 (1958), 125--148, doi:10.1007/BF02790232; Problem 7 on p. 142. The copy read is identified on the source card.

Read depth. Claims checked: the problem was read on the page image of p. 142 on 2026-10-08; the disk is printed without the bar the paper uses for closed disks. Nothing here is independently reviewed.

Dependencies

None.

Bears on

• #1048: the problem is Problem 7 with the zeros in the closed disk $|z|\le r$, where the paper's $D_r$ is the open disk $|z|<r$.