Theorems · Theorem · number theory
CuspFormClass.exp_decay_atImInfty
∀ {k : ℤ} {F : Type u_1} [inst : FunLike F UpperHalfPlane ℂ] {Γ : Subgroup (GL (Fin 2) ℝ)} {h : ℝ} (f : F)
[CuspFormClass F Γ k],
0 < h → h ∈ Γ.strictPeriods → ⇑f =O[UpperHalfPlane.atImInfty] fun τ => Real.exp (-2 * Real.pi * τ.im / h)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FunLikeCuspFormClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- AddSubgroupstatement · cited by 3,232
- Factproof · cited by 2,726
- FunLikestatement and proof · cited by 2,560
- Real.pistatement · cited by 1,774
- Real.expstatement · cited by 871
- UpperHalfPlanestatement and proof · cited by 626
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
Cited by1
Results whose statement or proof uses this declaration.
- CuspForm.exp_decay_isBigO_discriminantproof · cited by 0