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PreprintCC BY 4.0arXiv

Characterization of the boundary zero set of stable polynomials in ๐”น2

  • Dimitrios Vavitsas
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Abstract

Given a polynomial pโˆˆ โ„‚[z,w] whose zeros lie outside the unit ball ๐”น2 of โ„‚2, we study its local Weierstrass polynomial--obtained via the Weierstrass Preparation Theorem--and provide a strong version of the Nash curve selection lemma. These results lead to a characterization of the intersection of the zero set of p with the unit sphere: ๐’ต(p)โˆฉ๐•Š2.

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Cite

BibTeXRIS
BibTeX
@misc{vavitsas2026characterization,
  title = {{Characterization of the boundary zero set of stable polynomials in $\mathbb B_2$}},
  author = {Dimitrios Vavitsas},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02838},
  eprint = {2611.02838},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02838},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Characterization of the boundary zero set of stable polynomials in ๐”น_2
AU  - Dimitrios Vavitsas
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02838
UR  - https://arxiv.org/abs/2611.02838
AB  - Given a polynomial pโˆˆ โ„‚[z,w] whose zeros lie outside the unit ball ๐”น_2 of โ„‚^2, we study its local Weierstrass polynomial--obtained via the Weierstrass Preparation Theorem--and provide a strong version of the Nash curve selection lemma. These results lead to a characterization of the intersection of the zero set of p with the unit sphere: ๐’ต(p)โˆฉ๐•Š_2.
ER  -