OAI/NumberTheory/CubicMoment/Theta/CubicThetaAngularContinuity.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Locally uniform convergence for the fixed-angular theta expansion.
- lemma
OAI.CubicFirstMoment.cubicThetaAngular_continuousOn_stripline 9 - theorem
OAI.CubicFirstMoment.cubicThetaAngular_continuousAtline 41Source 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