Diophantine stability and second order terms
Number Theory
2024-09-19 v1
Abstract
We establish a Galois-theoretic trichotomy governing Diophantine stability for genus curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability . 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}
}