G functional eq real
G_functional_eq_real
Plain-language statement
G(1/s) = s^10 * (H₄(is))³ * (2(H₄(is))² + 5H₂(is)H₄(is) + 5(H₂(is))²)
Exact Lean statement
lemma G_functional_eq_real {s : ℝ} (hs : 0 < s) :
GReal (1 / s) = s ^ 10 * (H₄.resToImagAxis s).re ^ 3 *
(2 * (H₄.resToImagAxis s).re ^ 2 + 5 * (H₂.resToImagAxis s).re * (H₄.resToImagAxis s).re
+ 5 * (H₂.resToImagAxis s).re ^ 2)Formal artifact
Lean source
lemma G_functional_eq_real {s : ℝ} (hs : 0 < s) : GReal (1 / s) = s ^ 10 * (H₄.resToImagAxis s).re ^ 3 * (2 * (H₄.resToImagAxis s).re ^ 2 + 5 * (H₂.resToImagAxis s).re * (H₄.resToImagAxis s).re + 5 * (H₂.resToImagAxis s).re ^ 2) := by -- From G_functional_equation' and the fact that H₂, H₄ are real on imaginary axis have hG := G_functional_equation' hs rw [ResToImagAxis.Real.eq_real_part H₂_imag_axis_real s, ResToImagAxis.Real.eq_real_part H₄_imag_axis_real s] at hG exact_mod_cast hG- Project
- Sphere Packing in Dimension 8
- License
- Apache-2.0
- Commit
- acfc6204e65a
- Source
- SpherePacking/ModularForms/FG.lean:1163-1171
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Person-level attribution pending.
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Plain-language statement
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Source project: Sphere Packing in Dimension 8
Person-level attribution pending.
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Source project: Sphere Packing in Dimension 8
Person-level attribution pending.