The density of polynomials of degree n over Zp having exactly r roots in Qp
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.
Proceedings of the London Mathematical Society
London Mathematical Society
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).