Destagnol, K. and Sofos, E. (2019) Rational points and prime values of polynomials in moderately many variables. Bulletin des Sciences Mathématiques, 156, 102794. (doi: 10.1016/j.bulsci.2019.102794)
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Abstract
We derive the Hasse principle and weak approximation for fibrations of certain varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our varieties are defined through polynomials in many variables and part of our work is devoted to establishing Schinzel's hypothesis for polynomials of this kind. This last part is achieved by using arguments behind Birch's well-known result regarding the Hasse principle for complete intersections with the notable difference that we prove our result in 50% fewer variables than in the classical Birch setting. We also study the problem of square-free values of an integer polynomial with 66.6% fewer variables than in the Birch setting.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Sofos, Dr Efthymios |
Authors: | Destagnol, K., and Sofos, E. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Bulletin des Sciences Mathématiques |
Publisher: | Elsevier |
ISSN: | 0007-4497 |
ISSN (Online): | 1952-4773 |
Published Online: | 14 August 2019 |
Copyright Holders: | Copyright © 2019 Elsevier Masson SAS |
First Published: | First published in Bulletin des Sciences Mathématiques 156: 102794 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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