erdos_145.variants.le_eleven_thirds

Greaves, Harman, and Huxley [GHH97] showed that this is true for $0 \leq \alpha\leq 11/3$. [GHH97] Greaves, G. R. H. and Harman, G. and Huxley, M. N., Sieve Methods, Exponential Sums, and their Applications in Number Theory. (1997).

theorem erdos_145.variants.le_eleven_thirds {α : ℝ} (hα : α ∈ Set.Icc 0 (11 / 3)) :
    ∃ 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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