There is no degree independent Bombieri type inequality for non-homogeneous polynomials

J. M. Aldaz

There is no degree independent Bombieri type inequality for non-homogeneous polynomials

Classical Analysis and ODEs 2026-07-08 v1

Authors: J. M. Aldaz

Abstract

Bombieri's inequality for polynomials requires that at least one of them be homogeneous. In this note an AI provides a natural example showing that, as stated in the title, there is no degree independent Bombieri type inequality for non-homogeneous polynomials.

Keywords

Bombieri inequality non-homogeneous polynomials degree independent counterexample

Cite

@article{arxiv.2607.07482,
  title  = {There is no degree independent Bombieri type inequality for non-homogeneous polynomials},
  author = {J. M. Aldaz},
  journal= {arXiv preprint arXiv:2607.07482},
  year   = {2026}
}