arXiv Analytics

Sign in

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
arXiv:math/0504303 [math.NT] (Published 2005-04-14, updated 2006-04-04)
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
arXiv:1310.6219 [math.NT] (Published 2013-10-23, updated 2014-11-20)
The number of varieties in a family which contain a rational point