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theorem proved term proof

hadamardPartialProduct_zero

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formal statement (Lean)

  52@[simp] theorem hadamardPartialProduct_zero
  53    (zeros : ℕ → ℂ) (N : ℕ) :
  54    hadamardPartialProduct zeros 0 N = 1 := by

proof body

Term-mode proof.

  55  simp [hadamardPartialProduct]
  56
  57/-! ## 3. Exact Hadamard product data needed downstream -/
  58
  59/-- Hadamard product data for the pole-removed completed zeta.
  60
  61This is the real Track D target. The missing analytic work is the proof that
  62`completedRiemannZeta₀` has order at most one, that its zeros can be enumerated
  63with the required convergence properties, and that the corresponding genus-one
  64partial products converge to the pole-removed completed zeta up to `exp(A+B s)`.
  65-/

depends on (18)

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