Tom Fisher's Home Page

joint with Manjul Bhargava, John Cremona and Stevan Gajovic

We determine the probability that a random polynomial of degree n over Z_p has exactly r roots in Q_p, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.

The density of polynomials of degree n over Z_p having exactly r roots in Q_p   (19 pages)          

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