Schinzel Hypothesis on average and rational points

Abstract

We resolve Schinzel's Hypothesis (H) for $100\%$ of polynomials of arbitrary degree. We deduce that a positive proportion of diagonal conic bundles over $\mathbb{Q}$ with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Châtelet equations.

Cited by in corpus (2)

• On the Liouville function at polynomial arguments
• Polynomials represented by norm forms via the beta sieve