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

dc.contributor.author	Bhargava, Manjul
dc.contributor.author	Cremona, John
dc.contributor.author	Fisher, Thomas
dc.contributor.author	Gajovic, Stevan
dc.date.accessioned	2021-12-15T00:31:40Z
dc.date.available	2021-12-15T00:31:40Z
dc.identifier.issn	0024-6115
dc.identifier.uri	https://www.repository.cam.ac.uk/handle/1810/331408
dc.description.abstract	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.
dc.description.sponsorship	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).
dc.publisher	London Mathematical Society
dc.rights	All Rights Reserved
dc.rights.uri	http://www.rioxx.net/licenses/all-rights-reserved
dc.title	The density of polynomials of degree n over Zp having exactly r roots in Qp
dc.type	Article
dc.publisher.department	Department of Pure Mathematics And Mathematical Statistics
dc.date.updated	2021-12-13T23:06:14Z
prism.publicationName	Proceedings of the London Mathematical Society
dc.identifier.doi	10.17863/CAM.78861
dcterms.dateAccepted	2021-12-09
rioxxterms.version	AM
rioxxterms.type	Journal Article/Review
cam.orpheus.counter	32	*
cam.depositDate	2021-12-13
pubs.licence-identifier	apollo-deposit-licence-2-1
pubs.licence-display-name	Apollo Repository Deposit Licence Agreement
rioxxterms.freetoread.startdate	2024-12-14

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