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

Accepted version
Peer-reviewed

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Article

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Authors

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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Journal Title

Proceedings of the London Mathematical Society

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Journal ISSN

0024-6115

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Publisher

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).