Auxiliary Polynomial

Abstract

Construct a nonzero auxiliary polynomial with bounded index and logarithmic height.

Theorem 1.1 (Auxiliary Polynomial).

Lean statement: D5/S3/Arith/DiophantineApproximation/AuxiliaryPolynomial.exists_ne_zero_le_index_logHeight_le

Proof. Machine-checked in Lean as D5/S3/Arith/DiophantineApproximation/AuxiliaryPolynomial.exists_ne_zero_le_index_logHeight_le (✓ std3). ∎

Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.

Commentary.

Construct a nonzero auxiliary polynomial with bounded index and logarithmic height.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/AuxiliaryPolynomial.exists_ne_zero_le_index_logHeight_le
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/BombieriVaalerRelative
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma
• Dependency: D5/S3/Arith/DiophantineApproximation/AuxiliaryPolynomialFixedDegree
• Dependency: D5/S3/Arith/DiophantineApproximation/BoxMonomial
• Dependency: D5/S3/Arith/DiophantineApproximation/CountingVolume
• Dependency: D5/S3/Arith/DiophantineApproximation/MvHasseDeriv
• Dependency: D5/S3/Arith/DiophantineApproximation/PolynomialIndex