Theorems · Theorem · number theory
CuspFormClass.exists_bound
∀ {k : ℤ} {Γ : Subgroup (GL (Fin 2) ℝ)} [Γ.IsArithmetic] {F : Type u_2} [inst : FunLike F UpperHalfPlane ℂ]
[CuspFormClass F Γ k] (f : F), ∃ C, ∀ (τ : UpperHalfPlane), ‖f τ‖ ≤ C / τ.im ^ (↑k / 2)A weight k cusp form is bounded in norm by a constant multiple of (im τ) ^ (-k / 2).
- Defined in
- Mathlib.NumberTheory.ModularForms.Bounds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- FunLikestatement and proof · cited by 2,560
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- CuspFormClass.qExpansion_isBigOproof · cited by 1