Skorobogatov, A. N. and Sofos, E. (2023) Schinzel Hypothesis on average and rational points. Inventiones Mathematicae, 231(2), pp. 673-739. (doi: 10.1007/s00222-022-01153-6)
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Abstract
We resolve Schinzel’s Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over ℚ with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Châtelet equations.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Sofos, Dr Efthymios |
| Authors: | Skorobogatov, A. N., and Sofos, E. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Inventiones Mathematicae |
| Publisher: | Springer |
| ISSN: | 0020-9910 |
| ISSN (Online): | 1432-1297 |
| Published Online: | 28 September 2022 |
| Copyright Holders: | Copyright © 2022 The Authors |
| First Published: | First published in Inventiones Mathematicae 231(2): 673-739 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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