Gauss Lemma

Abstract

At a nonarchimedean place, the coefficient sup norm of a polynomial product is multiplicative.

Theorem 1.1 (Gauss Lemma).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma.iSup_coeff_mul

Proof. Machine-checked in Lean as D5/S3/Arith/AbsoluteValues/Heights/GaussLemma.iSup_coeff_mul (✓ std3). ∎

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

Commentary.

At a nonarchimedean place, the coefficient sup norm of a polynomial product is multiplicative.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma.iSup_coeff_mul
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/PseudoBasisMetrics