Theorems · Theorem · number theory
LSeries.term_convolution
∀ (f g : ℕ → ℂ) (s : ℂ) (n : ℕ), LSeries.term (LSeries.convolution f g) s n = ∑ p ∈ n.divisorsAntidiagonal, LSeries.term f s p.1 * LSeries.term g s p.2
We give an expression of the LSeries.term of the convolution of two functions
in terms of a sum over Nat.divisorsAntidiagonal.
- Defined in
- Mathlib.NumberTheory.LSeries.Convolution
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 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.
- Complexstatement and proof · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- eq_or_neproof · cited by 1,117
- Nat.cast_mulproof · cited by 309
- mul_div_assocproof · cited by 149
- Nat.divisorsAntidiagonalstatement and proof · cited by 61
- div_divproof · cited by 56
- LSeries.termstatement and proof · cited by 48
- Finset.sum_divproof · cited by 20
- LSeries.convolutionstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- LSeries.term_convolution'proof · cited by 1