OAI/NumberTheory/CubicMoment/Estimates/CubeRiesz.lean

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Identification of the actual cube-lattice integral with the model term.

  1. lemma OAI.CubicFirstMoment.normProfileFourier_cubing_integral line 14
  2. theorem OAI.CubicFirstMoment.cubeProfileIntegral_eq_model line 31

    Source documentation

    The exact Riesz constant for the trace pairing and covolume-one Eisenstein measure. All Fourier and singular-integral steps are proved.

    theorem cubeProfileIntegral_eq_model (W : ℝ → ℂ) (hW : HasCompactSupport W)
        (hW' : ContDiff ℝ ∞ W) :
        cubeProfileIntegral W = (cStar^2:ℝ) •
          ((2/Real.sqrt 3:ℝ) • (∫ z : ℂ, ((‖z‖^(-(2/3:ℝ)):ℝ):ℂ)*W (Complex.normSq z))) := by
    …

    Mentions: OAI.CubicFirstMoment.cubeProfileIntegral, OAI.CubicFirstMoment.cStar