Theorems · Theorem · number theory
ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div
∀ {q : ℕ} (a : ZMod q),
Summable fun n => (if Nat.Prime n then 0 else ArithmeticFunction.vonMangoldt.residueClass a n) / ↑nThe function n ↦ Λ n / n, restricted to non-primes in a residue class, is summable.
This is used to convert results on ArithmeticFunction.vonMangoldt.residueClass to results
on primes in an arithmetic progression.
- Defined in
- Mathlib.NumberTheory.LSeries.PrimesInAP
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- Equiv.symmproof · cited by 3,681
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- SProd.sprodproof · cited by 1,750
- le_rflproof · cited by 1,558
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_divproof · cited by 1