Finite Polynomial two columns norm le

Proved

D1Bound5.finitePolynomial_two_columns_norm_le

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finitePolynomial_two_columns_norm_le in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

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.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring

Formal statement

section
namespace D1Bound5



theorem _root_.D1Bound5.finitePolynomial_two_columns_norm_le (k d0 : ℕ)
    (p : Fin 2 → Fin (k+1) → ℂ) (v : Fin (k+1) → ℝ) (c : ℂ) (Y : ℝ)
    (hcoeff : ∀ ell, ‖p 0 ell‖+‖p 1 ell‖ ≤ v ell*Y^(d0+(ell : ℕ))) :
    ‖∑ ell, p 0 ell*c^(ell : ℕ)‖+‖∑ ell, p 1 ell*c^(ell : ℕ)‖ ≤
      Y^d0*∑ ell, v ell*(Y*‖c‖)^(ell : ℕ) := by sorry





end D1Bound5
end

Source

D1Bound5/FinitePolynomialHeight.lean, lines 16-39, SHA-256 0a57cf8e5e1b1bdad792f7fa018731c8a4bb1a5108b9cf615b3eb680734f76c5. Project: https://github.com/tomislav-math/d1-bound5-lean

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