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

Proceedings of the London Mathematical Society (2022) 124(5) 713-736
DOI: 10.1112/plms.12438
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Abstract

We determine the probability that a random polynomial of degree (Formula presented.) over (Formula presented.) has exactly (Formula presented.) roots in (Formula presented.), and show that it is given by a rational function of (Formula presented.) that is invariant under replacing (Formula presented.) by (Formula presented.).

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APA

Bhargava, M., Cremona, J., Fisher, T., & Gajović, S. (2022). The density of polynomials of degree nn over Zp having exactly r roots in Qp. Proceedings of the London Mathematical Society, 124(5), 713–736. https://doi.org/10.1112/plms.12438

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