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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1038.lean

Retained formal statement4 of 4

The infimum of |{x ∈ ℝ : |f x| < 1}| over all nonconstant monic polynomials f such that all of its roots are real and contained in [-1,1] is < 1.835.

FormalConjectures/ErdosProblems/1038.leanErdos1038.erdos_1038.variants.inf_upperBound1 lineExact file

1∀ (n : ℕ), ⨅ f, MeasureTheory.volume {x | |Polynomial.eval x ↑f| < 1} < 1.835

SolvedStatement only, no proof

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