Theorems · Theorem · number theory
bernoulliFun_mul
∀ (k : ℕ) {m : ℕ},
m ≠ 0 → ∀ (x : ℝ), bernoulliFun k (↑m * x) = ↑m ^ k / ↑m * ∑ i ∈ Finset.range m, bernoulliFun k (x + ↑i / ↑m)The multiplication theorem. Proof follows https://math.stackexchange.com/a/1721099/38218.
- Defined in
- Mathlib.NumberTheory.ZetaValues
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites64
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
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- add_commproof · cited by 1,535
- Finset.rangestatement and proof · cited by 1,341
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- pow_zeroproof · cited by 1,094
Cited by1
Results whose statement or proof uses this declaration.
- bernoulliFun_eval_halfproof · cited by 0