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A relative Schinzel-Zassenhaus bound for the polynomial T2 − 1

  • Alessio Cangini
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Abstract

For f(T) = T2 − 1, we establish a lower bound for the relative dynamical house of wandering algebraic integers. This bound depends on the degree over the maximal abelian extension of the rationals. Our proof follows Dimitrov's approach to the Schinzel-Zassenhaus Conjecture and its generalization by Habegger-Schmidt.

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Cite

BibTeXRIS
BibTeX
@misc{cangini2026relative,
  title = {{A relative Schinzel-Zassenhaus bound for the polynomial $T^2 - 1$}},
  author = {Alessio Cangini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28782},
  eprint = {2610.28782},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28782},
}
RIS
TY  - UNPB
TI  - A relative Schinzel-Zassenhaus bound for the polynomial T^2 − 1
AU  - Alessio Cangini
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28782
UR  - https://arxiv.org/abs/2610.28782
AB  - For f(T) = T^2 − 1, we establish a lower bound for the relative dynamical house of wandering algebraic integers. This bound depends on the degree over the maximal abelian extension of the rationals. Our proof follows Dimitrov's approach to the Schinzel-Zassenhaus Conjecture and its generalization by Habegger-Schmidt.
ER  -