Theorems · Theorem · number theory
EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq
∀ (z : UpperHalfPlane),
Filter.Tendsto (fun N => ∑ n ∈ Finset.Ico (-↑↑N) ↑↑N, ∑' (m : ℤ), (1 / (↑m * ↑z + ↑n) - 1 / (↑m * ↑z + ↑n + 1)))
Filter.atTop (nhds (-2 * ↑Real.pi * Complex.I / ↑z))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- MulZeroClass.mul_zeroproof · cited by 2,091
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- tsumstatement and proof · cited by 1,148
- Complex.Istatement and proof · cited by 866
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.tsum_symmetricIco_tsum_sub_eqproof · cited by 0