Lower bounds for ranks using Pell equations

P. G. Walsh

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arXiv · 2211.12138

Lower bounds for ranks using Pell equations

P. G. Walsh

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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.

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P. G. Walsh. 2022-11-22. Lower bounds for ranks using Pell equations. https://arxiv.org/abs/2211.12138

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