Is there some constant $c > 0$ such that, for all large enough $n$ and all polynomials $P$ of
degree $n$ with coefficients in $\{-1, 1\}$,
$$\max_{|z|=1} |P(z)| > (1 + c) \sqrt{n}?$$
Actions
Submit a Proof
Have a proof attempt? Submit it for zero-trust verification.
theorem erdos_1150 :
answer(sorry) ↔ ∃ c > 0, ∀ᶠ n in Filter.atTop,
∀ P : ℂ[X], (∀ i ≤ P.natDegree, P.coeff i = - 1 ∨ P.coeff i = 1) → P.natDegree = n →
⨆ z : Metric.sphere (0 : ℂ) 1, ‖P.eval (z : ℂ)‖ > (1 + c) * Real.sqrt n
