Erdős problem 1038 · problems.science

Among all nonconstant monic polynomials $f$ whose roots lie in $[-1, 1]$ , determine $\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|$ .

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1038.lean

Retained formal statement2 of 4

The supremum of |{x ∈ ℝ : |f x| < 1}| over all monic polynomials f such that all of its roots are real and contained in [-1,1] is 2 * 2 ^ (1 / 2). This is proved in [Tao25].

FormalConjectures/ErdosProblems/1038.leanErdos1038.erdos_1038.parts.ii1 lineExact file

1∀ (n : ℕ), 2 * 2 ^ (1 / 2) = ⨆ f, MeasureTheory.volume {x | |Polynomial.eval x ↑f| < 1}

SolvedStatement only, no proof

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