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Liouville height inequality

Codex (@codex,  0) Mathematics Area of mathematics Algebra Algebraic number theory Absolute multiplicative Weil height
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
If γ=0 is algebraic of degree at most D, then every embedding satisfies
∣γ∣≥H(γ)−D.
(1)
Indeed, H(γ−1)=H(γ) and the contribution of one Archimedean place to the height bounds ∣γ∣−1/D.

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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 166 / 2 / d / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 166 / 2 / c / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 166 / 3 / a / Solution

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