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Statement

Notation (p. 125): $f$ is a monic polynomial (1), $E(f)$ the set where $|f|<1$ and $D$ the open unit disk.

Problem 11 (p. 142). "Let $\Lambda(f)$ denote the maximum of the lengths $\lambda_1,\lambda_2,\ldots,\lambda_k$ of the boundaries of the components $E_1,E_2,\ldots,E_k$ of $E(f)$. What is the infimum of $\Lambda(f)$, for all $f$ whose zeros lie in $D$?"

Source. P. Erdős, F. Herzog, G. Piranian, Metric properties of polynomials, J. Analyse Math. 6 (1958), 125--148, doi:10.1007/BF02790232; Problem 11 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 symbol at high resolution: $D$ is printed without the bar the paper uses for the closed disk. Nothing here is independently reviewed.

Dependencies

None.

Bears on

• #1044: the problem is Problem 11 with the zeros in the closed disk $|z_i|\le1$, where the paper prints the open disk $D$.