Theorems · Theorem · sequences and series
Real.summable_one_div_int_pow
∀ {p : ℕ}, (Summable fun n => 1 / ↑n ^ p) ↔ 1 < pSummability of the p-series over ℤ.
- Defined in
- Mathlib.Analysis.PSeries
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- Int.cast_natCastproof · cited by 393
- Int.cast_negproof · cited by 224
- mul_powproof · cited by 220
- div_divproof · cited by 56
- Summable.mul_leftproof · cited by 47
- mul_one_divproof · cited by 45
- Nat.cast_injectiveproof · cited by 39
- Summable.comp_injectiveproof · cited by 22
- neg_eq_neg_one_mulproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- summable_bernoulli_fourierproof · cited by 1