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arXiv · 2005.02998

Schinzel Hypothesis on average and rational points

Alexei N. Skorobogatov·Efthymios Sofos
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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 Ch\^atelet equations.

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Alexei N. Skorobogatov, Efthymios Sofos. 2020-05-06. Schinzel Hypothesis on average and rational points. https://doi.org/10.1007/s00222-022-01153-6

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