Schinzel Hypothesis on average and rational points
Number Theory
2023-02-06 v3 Algebraic Geometry
Abstract
We resolve Schinzel's Hypothesis (H) for of polynomials of arbitrary degree. We deduce that a positive proportion of diagonal conic bundles over with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Ch\^atelet equations.
Cite
@article{arxiv.2005.02998,
title = {Schinzel Hypothesis on average and rational points},
author = {Alexei N. Skorobogatov and Efthymios Sofos},
journal= {arXiv preprint arXiv:2005.02998},
year = {2023}
}