Rational points and prime values of polynomials in moderately many variables

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
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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