Theorems · Theorem · number theory
LSeries_sum
∀ {ι : Type u_1} {f : ι → ℕ → ℂ} {S : Finset ι} {s : ℂ},
(∀ i ∈ S, LSeriesSummable (f i) s) → LSeries (∑ i ∈ S, f i) s = ∑ i ∈ S, LSeries (f i) s- Defined in
- Mathlib.NumberTheory.LSeries.Linearity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Complexstatement and proof · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- SummationFilter.unconditionalproof · cited by 2,068
- tsumproof · cited by 1,148
- LSeriesstatement · cited by 77
- LSeriesSummablestatement and proof · cited by 59
- LSeries.termproof · cited by 48
- Summable.tsum_finsetSumproof · cited by 5
- LSeries.term_sum_applyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.vonMangoldt.LSeries_residueClass_eqproof · cited by 1