Is it true that, if $A\subset \mathbb{Z}$ is a finite set of size $N$, then $$\int_0^1 \left\lvert \sum_{n\in A}e(n\theta)\right\rvert \mathrm{d}\theta \gg \log N,$$ where $e(x)=e^{2\pi ix }$?

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1True ↔2  ∃ c > 0, ∀ (N : ℕ) (A : Finset ℤ), A.card = N → c * Real.log ↑N ≤ ∫ (θ : ℝ) in 0..1, ‖∑ n ∈ A, additiveChar (↑n * θ)‖

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  Erdős AI contributions wiki · 22 Jun, 2026

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