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Statement

Notation (pp. 125, 142): $E$ is the set where $|f|<1$, and $f$ is a $K$-polynomial when $E$ is connected (see Theorem 10 for the definitions of Section 7).

Problem 14 (p. 143). "If $f$ is a $K$-polynomial, is $E$ contained in a disk of radius 2, and can the center of the disk be placed at the centroid of the zeros?"

Source. P. Erdős, F. Herzog, G. Piranian, Metric properties of polynomials, J. Analyse Math. 6 (1958), 125--148, doi:10.1007/BF02790232; Problem 14 on p. 143. The copy read is identified on the source card.

Read depth. Claims checked: the problem was read clause by clause on the page image of p. 143 on 2026-10-08. Nothing here is independently reviewed.

Dependencies

The definition of $K$-polynomials (p. 142).

Bears on

• #1046: the problem is the first question of Problem 14; the second, about centering the disk at the centroid of the zeros, is not in the problem's statement.