OAI/NumberTheory/CubicMoment/Estimates/CubeRiesz.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Identification of the actual cube-lattice integral with the model term.
- lemma
OAI.CubicFirstMoment.normProfileFourier_cubing_integralline 14 - theorem
OAI.CubicFirstMoment.cubeProfileIntegral_eq_modelline 31Source 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