Erdős Problem #1040
Prior state unknown→disproved
capacity alone does not determine the invariant; the zero-measure clause is a separate open question
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analysis / Potential Theory
Erdős Problem #1040
For a closed infinite set $F \subseteq \mathbb{C}$, let $\mu(F)$ be the infimum of $|\{z : |f(z)| < 1\}|$ over monic polynomials with zeros in $F$. Is $\mu(F)$ determined only by the transfinite diameter of $F$?
10Significance / 100
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For a closed infinite set $F \subseteq \mathbb{C}$, let $\mu(F)$ be the infimum of $|\{z : |f(z)| < 1\}|$ over monic polynomials with zeros in $F$. Is $\mu(F)$ determined only by the transfinite diameter of $F$?
capacity alone does not determine the invariant; the zero-measure clause is a separate open question
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