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PreprintCC BY 4.0arXiv

Counting Integral Matrices with Given Cubic Characteristic Polynomial

  • Philipp Habegger
Open at sourcePDFDOICite

Abstract

We show that the number of 3× 3 matrices with given characteristic polynomial and entries in ℤ∩ [−H,H] is at most c H3(log H)6 for all H≥ 2, where c>0 is an absolute constant.

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Cite

BibTeXRIS
BibTeX
@misc{habegger2026counting,
  title = {{Counting Integral Matrices with Given Cubic Characteristic Polynomial}},
  author = {Philipp Habegger},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34973},
  eprint = {2610.34973},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34973},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Counting Integral Matrices with Given Cubic Characteristic Polynomial
AU  - Philipp Habegger
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34973
UR  - https://arxiv.org/abs/2610.34973
AB  - We show that the number of 3× 3 matrices with given characteristic polynomial and entries in ℤ∩ [−H,H] is at most c H^3(log H)^6 for all H≥ 2, where c>0 is an absolute constant.
ER  -