Rational points and prime values of polynomials in moderately many variables

K.N. Destagnol, E. Sofos, Bulletin Des Sciences Mathematiques 156 (2019) 102794.


Journal Article | Epub ahead of print | English
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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.
Publishing Year
Date Published
2019-08-14
Journal Title
Bulletin des Sciences Mathematiques
Volume
156
Article Number
102794
ISSN
IST-REx-ID

Cite this

Destagnol KN, Sofos E. Rational points and prime values of polynomials in moderately many variables. Bulletin des Sciences Mathematiques. 2019;156:102794. doi:10.1016/j.bulsci.2019.102794
Destagnol, K. N., & Sofos, E. (2019). Rational points and prime values of polynomials in moderately many variables. Bulletin Des Sciences Mathematiques, 156, 102794. https://doi.org/10.1016/j.bulsci.2019.102794
Destagnol, Kevin N, and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” Bulletin Des Sciences Mathematiques 156 (2019): 102794. https://doi.org/10.1016/j.bulsci.2019.102794.
K. N. Destagnol and E. Sofos, “Rational points and prime values of polynomials in moderately many variables,” Bulletin des Sciences Mathematiques, vol. 156, p. 102794, 2019.
Destagnol KN, Sofos E. 2019. Rational points and prime values of polynomials in moderately many variables. Bulletin des Sciences Mathematiques. 156, 102794.
Destagnol, Kevin N., and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” Bulletin Des Sciences Mathematiques, vol. 156, Elsevier, 2019, p. 102794, doi:10.1016/j.bulsci.2019.102794.

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