Theorems · Definition · number theory
UpperHalfPlane.upperHalfPlaneSet
Set ℂ
The upper half plane as a subset of ℂ.
This is convenient for taking derivatives of functions on the upper half plane.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Complex.improof · cited by 591
Cited by25
Results whose statement or proof uses this declaration.
- UpperHalfPlane.isOpen_upperHalfPlaneSetstatement · cited by 14
- ModularForm.multipliableLocallyUniformlyOn_etastatement and proof · cited by 3
- ModularForm.differentiableAt_eta_tprodstatement and proof · cited by 2
- ModularForm.eta_ne_zerostatement and proof · cited by 2
- ModularForm.eta_tprod_ne_zerostatement and proof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_cexpstatement and proof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpstatement and proof · cited by 2
- UpperHalfPlane.range_coestatement · cited by 2
- ModularForm.one_sub_eta_q_ne_zerostatement and proof · cited by 2
- iteratedDerivWithin_tsum_cexp_eqstatement and proof · cited by 1
- ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSetstatement and proof · cited by 1
- ModularForm.summable_logDeriv_one_sub_eta_qstatement and proof · cited by 1