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

Stevan Gajovic, Manjul Bhargava, John Cremona, Tom Fisher

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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.
Original languageEnglish
Number of pages19
Publication statusSubmitted - 26-Jan-2021

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