OAI/NumberTheory/CubicMoment/Theta/CubicThetaAngularContinuity.lean

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Locally uniform convergence for the fixed-angular theta expansion.

  1. lemma OAI.CubicFirstMoment.cubicThetaAngular_continuousOn_strip line 9
  2. theorem OAI.CubicFirstMoment.cubicThetaAngular_continuousAt line 41

    Source documentation

    The fixed signed angular Fourier expansion is a continuous function at every point of the upper half-space.

    theorem cubicThetaAngular_continuousAt {a : Eisenstein → ℂ} {C : ℝ}
        (hC : 0 ≤ C) (ha : ∀ n : Eisenstein, n ≠ 0 → ‖a n‖ ≤ C*norm n)
        (ℓ : ℤ) {p : ℂ × ℝ} (hp : 0 < p.2) :
        ContinuousAt (cubicThetaNonconstant (cubicThetaAngularCoefficient a ℓ)) p := by
    …

    Mentions: OAI.CubicFirstMoment.Eisenstein, OAI.CubicFirstMoment.norm, OAI.CubicFirstMoment.cubicThetaNonconstant, OAI.CubicFirstMoment.cubicThetaAngularCoefficient