论文标题
重新审视通用的对角线圆锥捆
Generic diagonal conic bundles revisited
论文作者
论文摘要
我们证明，先前结果的一种更强的形式，即辛泽尔的假设以$ 100 \％的$ n $ t $ thupllass的整数多项式满足通常必要条件的$ 100 \％$ $，而多项式所代表的素数则由legendre符号的其他约束以及上限和下限。我们建立了射影线上的通用对角线圆锥捆的布劳尔群体的微不足道。最后，我们给出了明确的下限，以使某些自然家庭中的对角线圆锥形束具有合理点的可能性。
We prove a stronger form of our previous result that Schinzel's Hypothesis holds for $100\%$ of $n$-tuples of integer polynomials satisfying the usual necessary conditions, where the primes represented by the polynomials are subject to additional constraints in terms of Legendre symbols, as well as upper and lower bounds. We establish the triviality of the Brauer group of generic diagonal conic bundles over the projective line. Finally, we give an explicit lower bound for the probability that diagonal conic bundles in certain natural families have rational points.
