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Schinzel Hypothesis on average and rational points
Published 6 May 2020 in math.NT and math.AG | (2005.02998v3)
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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