OAI/NumberTheory/CubicMoment/Theta/CubicThetaArithmeticHorizontalTower.lean

GitHub source file

7 declarations, 0 contain sorry, 0 declared as axioms

The actual automorphic arithmetic theta section generates every nonzero angular series by its horizontal derivatives.

  1. def OAI.CubicFirstMoment.cubicThetaArithmeticHorizontalSlice line 12
  2. lemma OAI.CubicFirstMoment.cubicThetaArithmeticHorizontalSlice_eq line 15
  3. theorem OAI.CubicFirstMoment.cubicThetaArithmetic_positive_tower line 22
  4. theorem OAI.CubicFirstMoment.cubicThetaArithmetic_negative_tower line 30
  5. def OAI.CubicFirstMoment.cubicThetaArithmeticAngularAxis line 40

    Source documentation

    Extend the actual derivative on the positive vertical axis by zero. Only positive heights enter its Mellin transform.

    def cubicThetaArithmeticAngularAxis (ℓ : ℤ) (v : ℝ) : ℂ :=
…
  6. theorem OAI.CubicFirstMoment.cubicThetaArithmeticAngularAxis_eq line 46
  7. theorem OAI.CubicFirstMoment.cubicThetaArithmeticAngularAxis_completed line 59