The density of polynomials of degree n over Zp having exactly r roots in Qp
Proceedings of the London Mathematical Society
London Mathematical Society
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Bhargava, M., Cremona, J., Fisher, T., & Gajovic, S. The density of polynomials of degree n over Zp having exactly r roots in Qp. Proceedings of the London Mathematical Society https://doi.org/10.17863/CAM.78861
We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.
I did not receive any funding for this paper. See the acknowledgements section of the paper for funding received by my coauthors (none from the sources mentioned above).
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This record's DOI: https://doi.org/10.17863/CAM.78861
This record's URL: https://www.repository.cam.ac.uk/handle/1810/331408
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