Finite Homogeneous Two norm le ratio
ProvedD1Bound5.finiteHomogeneousTwo_norm_le_ratiodiophantine-tuplesnumber-theory
Retain the exact first-anchor ratio in each actual homogeneous coefficient polynomial, instead of replacing both anchor moduli by B.
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 import Definitions.Def_D1Bound5_FiniteHomogeneousRatio_Definitions import Definitions.Def_D1Bound5_FiniteHomogeneousTwo_Definitions
Formal statement
section
noncomputable section
namespace D1Bound5
theorem _root_.D1Bound5.finiteHomogeneousTwo_norm_le_ratio (n : ℕ) (v : Fin (n+1) → ℤ)
(x y : ℂ) (r : ℝ) (hr : 0 ≤ r) (hxy : ‖x‖ ≤ r*‖y‖) :
‖finiteHomogeneousTwo n v x y‖ ≤ finiteHomogeneousRatioWeight n v r*‖y‖^n := by sorry
end D1Bound5
end
Source
D1Bound5/FiniteHomogeneousRatio.lean, lines 14-32, SHA-256 15c96a58b594b4317eb87dac7d3be380eb2b464b0233e171dc57af6894fda59b. Project: https://github.com/tomislav-math/d1-bound5-lean