Theorems · Theorem · number theory
EisensteinSeries.hasSum_e2Summand_symmetricIco
∀ (z : UpperHalfPlane),
HasSum (fun x => EisensteinSeries.e2Summand x z)
(2 * riemannZeta 2 -
8 * ↑Real.pi ^ 2 *
∑' (n : ℕ+), ↑((ArithmeticFunction.sigma 1) ↑n) * Complex.exp (2 * ↑Real.pi * Complex.I * ↑z) ^ ↑n)
(SummationFilter.symmetricIco ℤ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Complexstatement · cited by 5,565
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- SummationFilter.unconditionalstatement · cited by 2,068
- Real.pistatement · cited by 1,774
- Complex.ofRealstatement · cited by 1,654
- tsumstatement · cited by 1,148
- Complex.Istatement · cited by 866
- UpperHalfPlanestatement and proof · cited by 626
- Complex.expstatement · cited by 612
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_e2Summand_symmetricIcoproof · cited by 1