论文标题
平均和理性点的菌泽尔假设
Schinzel Hypothesis on average and rational points
论文作者
论文摘要
我们以$ 100 \%的任意程度的多项式来解决Schinzel的假设(H)。 我们推断出,任何给定数量的退化纤维具有合理的点,对角圆锥束的正比例为$ \ mathbb {q} $具有合理的点,并获得了类似的广义巧克力室方程的结果。
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.