Theorems · Theorem · number theory
ArithmeticFunction.ofPowerSeries_pow
∀ {R : Type u_1} [inst : CommRing R] (q : ℕ) {k : ℕ},
k ≠ 0 →
∀ (f : PowerSeries R),
(ArithmeticFunction.ofPowerSeries (q ^ k)) f =
(ArithmeticFunction.ofPowerSeries q) (PowerSeries.subst (PowerSeries.X ^ k) f)In ArithmeticFunction.ofPowerSeries, replacing the base q with a power q ^ k corresponds
to substituting X with X ^ k in the original power series.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement · cited by 659
- PowerSeries.coeffproof · cited by 324
- ArithmeticFunctionstatement and proof · cited by 290
- pow_mulproof · cited by 210
- PowerSeries.Xstatement and proof · cited by 183
- PowerSeries.constantCoeffproof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.isMultiplicative_ofPowerSeries_of_isPrimePowproof · cited by 0