Theorems · Theorem · number theory
Nat.Primes.summable_rpow
∀ {r : ℝ}, (Summable fun p => ↑↑p ^ r) ↔ r < -1The series over p^r for primes p converges if and only if r < -1.
- Defined in
- Mathlib.NumberTheory.SumPrimeReciprocals
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
- Summablestatement and proof · cited by 778
- one_divproof · cited by 624
- Subtype.propproof · cited by 505
- not_ltproof · cited by 306
- Nat.cast_nonneg'proof · cited by 245
- Nat.Prime.one_ltproof · cited by 118
- Nat.Primesstatement and proof · cited by 63
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpowproof · cited by 1