Erdős problem 119 · problems.science

For unit-modulus complex numbers $z_i$ , let $p_n(z)=\prod_{i\le n}(z-z_i)$ and $M_n=\max_{|z|=1}|p_n(z)|$ . Erdős's prize question: is there $c>0$ with $\sum_{k\le n} M_k > n^{1+c}$ ?

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

119.lean

Retained formal statement2 of 3

Is it true that there exists $c > 0$ such that for infinitely many $n$ we have $M_n > n^c$ ?

The second question was answered by Beck [Be91], who proved that there exists some $c>0$ such that $\max_{n\leq N} M_n > N^c$ .

FormalConjectures/ErdosProblems/119.leanErdos119.erdos_119.parts.ii1 lineExact file

1True ↔ ∀ (z : ℕ → ℂ), (∀ (i : ℕ), ‖z i‖ = 1) → ∃ c, ∃ (_ : c > 0), Infinite ↑{n | Erdos119.M z n > ↑n ^ c}

SolvedStatement only, no proof

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