English

Lower bounds for ranks using Pell equations

Number Theory 2022-11-23 v1

Abstract

We examine the ranks of a subfamily of curves in a previous article, which are derived from the existence of solutions to certain Pell equations. We exhibit an abundance of curves of moderately large rank, and prove under mild conditions that these curves have rank at least three.

Keywords

Cite

@article{arxiv.2211.12138,
  title  = {Lower bounds for ranks using Pell equations},
  author = {P. G. Walsh},
  journal= {arXiv preprint arXiv:2211.12138},
  year   = {2022}
}

Comments

4 pages

R2 v1 2026-06-28T06:34:28.081Z