erdos_119.parts.ii

Question 2: Is it true that there exists $c > 0$ such that for infinitely many $n$ we have $M_n > n^c$? Beck [Be91] proved that there exists some $c > 0$ such that $\max_{n \leq N} M_n > N^c$. [Be91] Beck, J., The modulus of polynomials with zeros on the unit circle: A problem of Erdős. Annals of Math. (1991), 609-651.

theorem erdos_119.parts.ii :
    answer(True) ↔ ∀ (z : ℕ → ℂ) (hz : ∀ i : ℕ, ‖z i‖ = 1),
      ∃ (c : ℝ) (hc : c > 0), Infinite {n : ℕ | M z n > n ^ c}

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