Theorems · Theorem · number theory
ModularForm.differentiableAt_eta_tprod
∀ {z : ℂ},
z ∈ UpperHalfPlane.upperHalfPlaneSet → DifferentiableAt ℂ (fun x => ∏' (n : ℕ), (1 - ModularForm.eta_q n x)) z- Cited by
- 2 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement · cited by 2,068
- Metric.ballproof · cited by 735
- DifferentiableAtstatement · cited by 617
- IsOpen.mem_nhdsproof · cited by 470
- tprodstatement · cited by 230
- dist_zero_rightproof · cited by 172
- Metric.isOpen_ballproof · cited by 63
- Function.Periodic.qParamproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- ModularForm.logDeriv_eta_eq_E2proof · cited by 1
- ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSetproof · cited by 1