Theorems · Theorem · number theory
EisensteinSeries.tendsto_double_sum_S_act
∀ (z : UpperHalfPlane),
Filter.Tendsto (fun N => ∑' (n : ℤ), ∑ m ∈ Finset.Ico (-↑N) ↑N, 1 / (↑n * ↑z + ↑m) ^ 2) Filter.atTop
(nhds ((↑z ^ 2)⁻¹ * EisensteinSeries.G2 (ModularGroup.S • z)))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 314 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetproof · cited by 13,712
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Finset.sumstatement and proof · cited by 5,195
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Matrix.vecEmptyproof · cited by 832
- Filter.mapproof · cited by 819
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.tsum_symmetricIco_tsum_eq_S_actproof · cited by 0