There is no degree independent Bombieri type inequality for non-homogeneous polynomials
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.
Disclosure
“m→∞ As the main author of this note is Gemini (my contribution having been to check the details and make the presentation suit my taste) this ms. will not be submitted to a journal for publication. Also, I used Gemini because it is the LLM that pops out when I open the Chrome navigator, and so far utilizing it has not cost me any money. But I have no financial interest in Gemini or any other AI. Finally, it seems that thinking first and asking an AI second, at least in this”
PDF page 2
- Classification
- Substantial mathematical content or result generation
- Multiplier
- 10
- Verified
Structural counts
Pages 3 pdf
Theorems 1 source
Lemmas 0 source
Propositions 0 source
Corollaries 0 source
Definitions 0 source
Displayed equations 7 source
Bibliography entries 2 source
Appendix pages 0 estimated
Count notes
- Source counts use the expanded primary TeX file Non_BombieriForPolys_ArXiv.tex.
- Appendix pages include the first PDF page with an explicit Appendix heading through the final page.