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

Manjul Bhargava, John Cremona, Tom Fisher, Stevan Gajović

Research output: Contribution to journalArticlepeer-review

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.).

Original languageEnglish (US)
JournalProceedings of the London Mathematical Society
DOIs
StateAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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