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Theorems · Theorem · number theory

OnePoint.isBoundedAt_iff

∀ {c : OnePoint ℝ} {f : UpperHalfPlane → ℂ} {k : ℤ} {g : GL (Fin 2) ℝ},
  g • OnePoint.infty = c → (c.IsBoundedAt f k ↔ UpperHalfPlane.IsBoundedAtImInfty (SlashAction.map k g f))

To check that f is bounded at c, it suffices for f ∣[k] g to be bounded at ∞ for any single g with g • ∞ = c.

Defined in
Mathlib.NumberTheory.ModularForms.BoundedAtCusp
Cited by
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Foundations
Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
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Real · cited by 25697RealComplex · cited by 5565ComplexMatrix · cited by 4303MatrixUpperHalfPlane · cited by 626UpperHalfPlaneMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupOnePoint · cited by 126OnePointOnePoint.infty · cited by 102OnePoint.inftySlashAction.map · cited by 74SlashAction.mapUpperHalfPlane.IsBoundedAtImInfty · cited by 30UpperHalfPlane.IsBoundedA…OnePoint.IsBoundedAt · cited by 12OnePoint.IsBoundedAtOnePoint.isBoundedAt_iffCITED BYCITES

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