arXiv:2005.02998 [math.NT]AbstractReferencesReviewsResources
Schinzel Hypothesis with probability 1 and rational points
Alexei N. Skorobogatov, Efthymios Sofos
Published 2020-05-06Version 1
We prove the existence version of Schinzel's Hypothesis (H) for $100\%$ of integer polynomials $P_1, \ldots, P_n$ of fixed degrees, when ordered by the size of coefficients. 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.
Related articles: Most relevant | Search more
A conjecture on rational approximations to rational points
arXiv:2212.10373 [math.NT] (Published 2022-12-20)
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
The number of varieties in a family which contain a rational point