erdos_145.variants.le_two

Erdős [Er51] proved this for all $0\leq \alpha\leq 2$. [Er51] Erdös, P., Some problems and results in elementary number theory. Publ. Math. Debrecen (1951), 103-109.

theorem erdos_145.variants.le_two {α : ℝ} (hα : α ∈ Set.Icc 0 2) :
    ∃ β : ℝ,
      atTop.Tendsto (fun x : ℝ ↦ 1 / x * ∑ n ∈ A x, (s (n + 1) - s n : ℝ) ^ α) (𝓝 β)

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