Theorems · Theorem · number theory
Rat.logHeight_eq_max_abs_of_gcd_eq_one
∀ {ι : Type u_1} [inst : Fintype ι] [Nonempty ι] {x : ι → ℤ},
Finset.univ.gcd x = 1 → Height.logHeight (Int.cast ∘ x) = Real.log ↑(⨆ i, |x i|)The logarithmic height of a tuple of rational numbers that consists of coprime integers is the logarithm of the maximum of the absolute values of the entries.
- Defined in
- Mathlib.NumberTheory.Height.NumberField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- iSupstatement and proof · cited by 2,415
- absstatement and proof · cited by 1,814
- Real.logstatement and proof · cited by 939
- Finset.gcdstatement and proof · cited by 49
- Height.logHeightstatement · cited by 35
- Rat.mulHeight_eq_max_abs_of_gcd_eq_oneproof · cited by 2
- Height.logHeight_eq_log_mulHeightproof · cited by 2
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