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PreprintCC BY 4.0arXiv

Some arithmetical aspects of the two dimensional Jacobian Conjecture

  • Ronen Peretz
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Abstract

We prove that any counter-example to the two dimensional Jacobian Conjecture with integral coefficients and determinant of its Jacobian matrix equals one, has only paths of asymptotic values that can contain only finitely many points of the planar integral lattice. The second part of our paper gives some nontrivial applications of the theory of certain Theta functions to the two dimensional Jacobian Conjecture over the real field, and over the complex field.

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Cite

BibTeXRIS
BibTeX
@misc{peretz2026some,
  title = {{Some arithmetical aspects of the two dimensional Jacobian Conjecture}},
  author = {Ronen Peretz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02961},
  eprint = {2610.02961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02961},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Some arithmetical aspects of the two dimensional Jacobian Conjecture
AU  - Ronen Peretz
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.02961
UR  - https://arxiv.org/abs/2610.02961
AB  - We prove that any counter-example to the two dimensional Jacobian Conjecture with integral coefficients and determinant of its Jacobian matrix equals one, has only paths of asymptotic values that can contain only finitely many points of the planar integral lattice. The second part of our paper gives some nontrivial applications of the theory of certain Theta functions to the two dimensional Jacobian Conjecture over the real field, and over the complex field.
ER  -