Theorems · Theorem · number theory
Height.logHeight_pow
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_2} [Finite ι] (x : ι → K) (n : ℕ),
Height.logHeight (x ^ n) = ↑n * Height.logHeight xThe logarithmic height of the coordinate-wise nth power of a tuple
is n times its logarithmic height.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- Real.logproof · cited by 939
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.mulHeightproof · cited by 64
- Height.logHeightstatement · cited by 35
- Real.log_powproof · cited by 29
- Height.mulHeight_powproof · cited by 3
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