The density of polynomials of degree n over Zp having exactly r roots in Qp
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Bhargava, Manjul
Cremona, John
Fisher, Thomas
Gajovic, Stevan
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.
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Proceedings of the London Mathematical Society
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0024-6115
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London Mathematical Society
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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).