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Theorems · Theorem · number theory

ModularForm.eta_ne_zero

∀ {z : ℂ}, z ∈ UpperHalfPlane.upperHalfPlaneSet → ModularForm.eta z ≠ 0

Eta is non-vanishing on the upper half plane.

Defined in
Mathlib.NumberTheory.ModularForms.DedekindEta
Cited by
2 results in Mathlib
Foundations
Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ModularForm.discriminant_ne_zero · cited by 2ModularForm.discriminant_…E2_mdifferentiable · cited by 1E2_mdifferentiableSet · cited by 53352SetComplex · cited by 5565Complexmul_ne_zero · cited by 178mul_ne_zeroUpperHalfPlane.upperHalfPlaneSet · cited by 25UpperHalfPlane.upperHalfP…ModularForm.eta · cited by 6ModularForm.etaFunction.Periodic.qParam_ne_zero · cited by 3Periodic.qParam_ne_zeroModularForm.eta_tprod_ne_zero · cited by 2ModularForm.eta_tprod_ne_…ModularForm.eta_ne_zeroCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.