Power-free values of polynomials on symmetric varieties

T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society 114 (2017) 1044–1080.


Journal Article | Published
Author
;
Abstract
Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics defined over Q.
Publishing Year
Date Published
2017-06-01
Journal Title
Proceedings of the London Mathematical Society
Acknowledgement
While working on this paper the authors were supported by ERC grants 306457 and 239606, respectively.
Volume
114
Issue
6
Page
1044 - 1080
IST-REx-ID

Cite this

Browning TD, Gorodnik A. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 2017;114(6):1044-1080. doi:10.1112/plms.12030
Browning, T. D., & Gorodnik, A. (2017). Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society, 114(6), 1044–1080. https://doi.org/10.1112/plms.12030
Browning, Timothy D, and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” Proceedings of the London Mathematical Society 114, no. 6 (2017): 1044–80. https://doi.org/10.1112/plms.12030.
T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” Proceedings of the London Mathematical Society, vol. 114, no. 6, pp. 1044–1080, 2017.
Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080.
Browning, Timothy D., and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” Proceedings of the London Mathematical Society, vol. 114, no. 6, Wiley Blackwell, 2017, pp. 1044–80, doi:10.1112/plms.12030.

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