18 lines
534 B
Plaintext
18 lines
534 B
Plaintext
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import Nevanlinna.holomorphic_JensenFormula
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open Real
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variable {f : ℂ → ℂ}
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variable {h₁f : AnalyticOn ℂ f ⊤}
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variable {h₂f : f 0 ≠ 0}
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noncomputable def unintegratedCounting : ℝ → ℕ := by
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intro r
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let A := h₁f.mono (by tauto : Metric.closedBall (0 : ℂ) r ⊆ ⊤)
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exact ∑ᶠ z, (A.order z).toNat
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noncomputable def integratedCounting : ℝ → ℝ := by
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intro r
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-- Issue here: for s on the boundary of the ball, zero comes out.
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exact ∑ᶠ s, (h₁f.order s).toNat * log (r * ‖s.1‖⁻¹)
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