Theorems · Theorem · sequences and series
Complex.summable_one_div_nat_cpow
∀ {p : ℂ}, (Summable fun n => 1 / ↑n ^ p) ↔ 1 < p.re- Defined in
- Mathlib.Analysis.PSeriesComplex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.unconditionalstatement and proof · cited by 2,068
- Complex.ofRealproof · cited by 1,654
- Complex.restatement and proof · cited by 882
- Summablestatement and proof · cited by 778
- NormOneClass.norm_oneproof · cited by 148
- Nat.cast_posproof · cited by 113
- norm_divproof · cited by 53
- summable_nat_add_iffproof · cited by 24
- Complex.norm_cpow_eq_rpow_re_of_posproof · cited by 21
- summable_norm_iffproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- zeta_eq_tsum_one_div_nat_add_one_cpowproof · cited by 3