Mathlib Map

Theorems · Inductive type · number theory

UpperHalfPlane

Type

The open upper half plane, denoted as ℍ within the UpperHalfPlane namespace

Defined in
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
Cited by
626 results in Mathlib
Foundations
Depth 0 from the axioms, rests on 1 definitions · uses no axioms
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Around this declaration

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

UpperHalfPlane.coe · cited by 288UpperHalfPlane.coeUpperHalfPlane.im · cited by 128UpperHalfPlane.imModularFormClass · cited by 64ModularFormClassUpperHalfPlane.qExpansion · cited by 64UpperHalfPlane.qExpansionUpperHalfPlane.re · cited by 63UpperHalfPlane.reUpperHalfPlane.im_pos · cited by 62UpperHalfPlane.im_posUpperHalfPlane.ofComplex · cited by 59UpperHalfPlane.ofComplexUpperHalfPlane.cuspFunction · cited by 46UpperHalfPlane.cuspFuncti…UpperHalfPlane.atImInfty · cited by 35UpperHalfPlane.atImInftyUpperHalfPlane.IsBoundedAtImInfty · cited by 30UpperHalfPlane.IsBoundedA…UpperHalfPlane.IsZeroAtImInfty · cited by 24UpperHalfPlane.IsZeroAtIm…CuspFormClass · cited by 21CuspFormClassModularForm.discriminant · cited by 20ModularForm.discriminantSlashInvariantFormClass · cited by 20SlashInvariantFormClassUpperHalfPlane.center · cited by 20UpperHalfPlane.centerUpperHalfPlaneCITED BYCITES

Cites0

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

Nothing in Mathlib beyond the foundations.

Cited by712

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 712.