Theorems · Theorem · number theory
EisensteinSeries.G2_S_transform
∀ (z : UpperHalfPlane), EisensteinSeries.G2 z = (↑z ^ 2)⁻¹ * EisensteinSeries.G2 (ModularGroup.S • z) - -2 * ↑Real.pi * Complex.I / ↑z
This is the key identity for how G2 transforms under the slash action by S.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- SummationFilter.unconditionalproof · cited by 2,068
- Real.pistatement · cited by 1,774
- Complex.ofRealstatement · cited by 1,654
- tsumproof · cited by 1,148
- Complex.Istatement · cited by 866
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- UpperHalfPlanestatement and proof · cited by 626
- Matrix.SpecialLinearGroupstatement · cited by 348
- UpperHalfPlane.coestatement · cited by 288
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.G2_slash_actionproof · cited by 1