Research proof index

H₂, H₃, H₄ are modular forms of weight 2 and level Γ(2) -/ noncomputable def H₂_SIF : SlashInvariantForm (Γ 2) 2 where toFun := H₂ slash_action_eq' := slashaction_generators_Γ2 H₂ (2 : ℤ) H₂_α_action H₂_β_action H₂_negI_action noncomputable def H₃_SIF : SlashInvariantForm (Γ 2) 2 where toFun := H₃ slash_action_eq' := slashaction_generators_Γ2 H₃ (2 : ℤ) H...

lim_{t→∞} L₁,₀(it)/(F(it)G(it)) = 1/2.

If F z / exp(a·z) → C ≠ 0 at i∞, then D F / F → a/(2πi): the exponential contributes a/(2πi) and the bounded limit factor's log-derivative vanishes. Public so downstream files (e.g. #331's Θ₂ analysis) can reuse it.

Division of MDifferentiable functions on ℍ is MDifferentiable, when the denominator is everywhere nonzero.

A modular form tends to its value at infinity as z → i∞.

If g(t₀) = 0 and deriv g t₀ < 0, then g is negative shortly after t₀.