English

Diophantine stability and second order terms

Number Theory 2024-09-19 v1

Abstract

We establish a Galois-theoretic trichotomy governing Diophantine stability for genus 00 curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability 11. Our asymptotic formula for the second order term exhibits strong bias towards instability.

Keywords

Cite

@article{arxiv.2409.12144,
  title  = {Diophantine stability and second order terms},
  author = {Carlo Pagano and Efthymios Sofos},
  journal= {arXiv preprint arXiv:2409.12144},
  year   = {2024}
}
R2 v1 2026-06-28T18:49:17.465Z