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ZetaBnd_aux1p fix
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AlexKontorovich committed Jan 28, 2025
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2 changes: 1 addition & 1 deletion PrimeNumberTheoremAnd/ZetaBounds.lean
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Expand Up @@ -754,7 +754,7 @@ $$
$$
\end{lemma}
%%-/
lemma ZetaBnd_aux1p (N : ℕ) (Npos : 1 ≤ N) {σ t : ℝ} (hσ : σ ∈ Ioc 0 2) (ht : 2 ≤ |t|) :
lemma ZetaBnd_aux1p (N : ℕ) (Npos : 1 ≤ N) {σ : ℝ} (hσ : σ ∈ Ioc 0 2) :
(fun (t : ℝ) ↦ ‖(σ + t * I) * ∫ x in Ioi (N : ℝ), (⌊x⌋ + 1 / 2 - x) / (x : ℂ) ^ ((σ + t * I) + 1)‖)
=O[Filter.principal {t | 2 ≤ |t|}] fun t ↦ |t| * N ^ (-σ) / σ := by
rw [Asymptotics.IsBigO_def]
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