English

A note on pencils of norm-form equations

Number Theory 2021-04-13 v1

Abstract

We find all solutions to the parametrized family of norm-form equations x3(t31)y3+3(t31)xy+(t31)2=±1x^3-(t^3-1)y^3+3(t^3-1)xy+(t^3-1)^2 = \pm 1 studied by Amoroso, Masser and Zannier. Our proof relies upon an appeal to lower bounds for linear forms in logarithms and various elementary arguments.

Cite

@article{arxiv.2104.04544,
  title  = {A note on pencils of norm-form equations},
  author = {Prajeet Bajpai and Michael A. Bennett},
  journal= {arXiv preprint arXiv:2104.04544},
  year   = {2021}
}
R2 v1 2026-06-24T01:01:11.078Z