Theorems · Theorem · number theory

UpperHalfPlane.hasSum_qExpansion

∀ {h : ℝ} {f : UpperHalfPlane → ℂ},
  0 < h →
    Function.Periodic (f ∘ ↑UpperHalfPlane.ofComplex) ↑h →
      MDiff f →
        UpperHalfPlane.IsBoundedAtImInfty f →
          ∀ (τ : UpperHalfPlane),
            HasSum (fun m => (PowerSeries.coeff m) (UpperHalfPlane.qExpansion h f) • Function.Periodic.qParam h ↑τ ^ m)
              (f τ)

Defined in: Mathlib.NumberTheory.ModularForms.QExpansion
Cited by: 2 results in Mathlib
Foundations: Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites26

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
RingHom.idstatement · cited by 18,349
LinearMapstatement · cited by 10,215
Complexstatement and proof · cited by 5,565
Norm.normproof · cited by 5,413
SummationFilter.unconditionalstatement and proof · cited by 2,068
Complex.ofRealstatement and proof · cited by 1,654
LT.lt.ne'proof · cited by 1,417
modelWithCornersSelfstatement and proof · cited by 920
PowerSeriesstatement · cited by 797
OpenPartialHomeomorph.toFun'statement and proof · cited by 745

Cited by2

Results whose statement or proof uses this declaration.

UpperHalfPlane.qExpansion_eq_zero_iffproof · cited by 1
ModularForm.hasSum_qExpansionproof · cited by 0