HadamardFactorizationStatus

formal source

  92
  93/-- Practical Track D bundle: the proved Mathlib inputs plus the open Hadamard
  94product data type. -/
  95structure HadamardFactorizationStatus where
  96  completed_zeta0_entire :
  97    Differentiable ℂ completedRiemannZeta₀
  98  completed_zeta0_functional_equation :
  99    ∀ s : ℂ, completedRiemannZeta₀ s = completedRiemannZeta₀ (1 - s)
 100  hadamard_data_to_product :
 101    ∀ data : CompletedZetaHadamardProduct,
 102      ∀ s : ℂ,
 103        completedRiemannZeta₀ s =
 104          Complex.exp (data.A + data.B * s) * data.productLimit s
 105
 106def hadamardFactorizationStatus : HadamardFactorizationStatus where
 107  completed_zeta0_entire := completedZeta0_differentiable
 108  completed_zeta0_functional_equation := completedZeta0_functional_equation
 109  hadamard_data_to_product := completedRiemannZeta0_hadamard_product
 110
 111end
 112
 113end HadamardFactorization
 114end NumberTheory
 115end IndisputableMonolith