Thue equations that simultaneously fail the Hasse principle
Number Theory
2026-07-06 v1
Abstract
We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x; y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree >2 and are ordered by the absolute value of the maximum of the coefficients.
Cite
@article{arxiv.2607.05234,
title = {Thue equations that simultaneously fail the Hasse principle},
author = {Paloma Bengoechea},
journal= {arXiv preprint arXiv:2607.05234},
year = {2026}
}