Theorems · Theorem · field theory
norm_zpow
∀ {α : Type u_2} [inst : NormedDivisionRing α] (a : α) (n : ℤ), ‖a ^ n‖ = ‖a‖ ^ n- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- NormedDivisionRingstatement and proof · cited by 360
- map_zpow₀proof · cited by 26
- normHomproof · cited by 8
Cited by18
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_norm_eisSummandproof · cited by 4
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- MeromorphicOn.extract_zeros_poles_logproof · cited by 3
- Seminorm.rescale_to_shell_zpowproof · cited by 2
- UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_leftproof · cited by 2
- ModularFormClass.exists_petersson_leproof · cited by 1
- UpperHalfPlane.IsZeroAtImInfty.slashproof · cited by 1
- EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIFproof · cited by 1
- Padic.norm_p_zpowproof · cited by 1
- CuspFormClass.exists_boundproof · cited by 1
- PeriodPair.hasSum_sumInvPowproof · cited by 1
- Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAtproof · cited by 1