Theorems · Theorem · number theory
EisensteinSeries.hasSum_e2Summand_symmetricIcc
∀ (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.symmetricIcc ℤ)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 309 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 and proof · cited by 62,936
- Finsetproof · cited by 13,712
- Complexstatement · cited by 5,565
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Finset.rangeproof · cited by 1,341
- tsumstatement and proof · cited by 1,148
Cited by3
Results whose statement or proof uses this declaration.
- EisensteinSeries.G2_eq_tsum_cexpproof · cited by 3
- EisensteinSeries.summable_e2Summand_symmetricIccproof · cited by 2
- EisensteinSeries.hasSum_e2Summand_symmetricIcoproof · cited by 1