The density of polynomials of degree n over Zp having exactly r roots in Qp

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Authors
Bhargava, Manjul
Cremona, John
Fisher, Thomas
Gajovic, Stevan
Journal Title
Proceedings of the London Mathematical Society
ISSN
0024-6115
Publisher
London Mathematical Society
Type
Article
This Version
AM
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Citation
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
Abstract
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.
Sponsorship
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).
Embargo Lift Date
2024-12-14
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.78861
This record's URL: https://www.repository.cam.ac.uk/handle/1810/331408
Rights
All Rights Reserved
Licence URL: http://www.rioxx.net/licenses/all-rights-reserved
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