OAI/NumberTheory/CubicMoment/Theta/CubicThetaComplexHeight.lean

GitHub source file

11 declarations, 0 contain sorry, 0 declared as axioms

Holomorphic dependence of the Fourier heat integral on a complex height with positive real part. All majorants are actual heat integrals.

  1. def OAI.CubicFirstMoment.cubicThetaComplexHeightHeat line 12
  2. def OAI.CubicFirstMoment.cubicThetaHeightMajorant line 15
  3. lemma OAI.CubicFirstMoment.cubicThetaComplexHeightHeat_norm line 18
  4. lemma OAI.CubicFirstMoment.cubicThetaHeightMajorant_eq line 24
  5. lemma OAI.CubicFirstMoment.cubicThetaHeightMajorant_integrable line 33
  6. lemma OAI.CubicFirstMoment.cubicThetaHeightDerivative_integrable line 39
  7. lemma OAI.CubicFirstMoment.cubicThetaComplexHeightHeat_bound line 65
  8. lemma OAI.CubicFirstMoment.cubicThetaComplexHeightHeat_deriv line 74
  9. def OAI.CubicFirstMoment.cubicThetaComplexHeightIntegral line 84
  10. lemma OAI.CubicFirstMoment.cubicThetaComplexHeightIntegral_differentiableAt line 87
  11. theorem OAI.CubicFirstMoment.cubicThetaComplexHeightIntegral_analytic line 126