Finite Homogeneous Two norm le

Proved

D1Bound5.finiteHomogeneousTwo_norm_le

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The usual coefficient sum bounds the actual homogeneous polynomial. No coefficient or polynomial-height certificate is assumed.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteHomogeneousTwo_Definitions

Formal statement

section
namespace D1Bound5




theorem _root_.D1Bound5.finiteHomogeneousTwo_norm_le (n : ℕ) (v : Fin (n+1) → ℤ)
    (x y : ℂ) (hxy : ‖x‖ ≤ ‖y‖) :
    ‖finiteHomogeneousTwo n v x y‖ ≤
      (∑ j, |(v j : ℝ)|)*‖y‖^n := by sorry



end D1Bound5
end

Source

D1Bound5/FiniteHomogeneousTwo.lean, lines 15-34, SHA-256 0f528bdfa4bbe6e6461cbf40c954a5b8c6a03faf9be9e291dd140696bc0e3dfa. Project: https://github.com/tomislav-math/d1-bound5-lean

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