Theorems · Theorem · number theory
ModularForm.mul_ne_zero
∀ {Γ : Subgroup (GL (Fin 2) ℝ)} [inst : Γ.HasDetPlusMinusOne],
(∃ h ∈ Γ.strictPeriods, 0 < h) → ∀ {a b : ℤ} {f : ModularForm Γ a} {g : ModularForm Γ b}, f ≠ 0 → g ≠ 0 → f.mul g ≠ 0The product of two non-zero modular forms is non-zero.
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- Foundations
- Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.HasDetPlusMinusOne
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- AddSubgroupstatement · cited by 3,232
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- mul_ne_zeroproof · cited by 178
- ModularFormstatement and proof · cited by 98
- Subgroup.strictPeriodsstatement and proof · cited by 63
- Subgroup.HasDetPlusMinusOnestatement and proof · cited by 57
- ModularForm.mulstatement and proof · cited by 6
- ModularForm.qExpansion_mulproof · cited by 4
- ModularForm.qExpansion_eq_zero_iffproof · cited by 1
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