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hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCARUSO, Xavier
dc.date.accessioned2024-04-04T02:45:17Z
dc.date.available2024-04-04T02:45:17Z
dc.date.created2021-10
dc.date.issued2022-07
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191453
dc.description.abstractEnWe study the repartition of the roots of a random p-adic polynomial in an algebraic closure of Qp.We prove that the mean number of roots generating a fixed finite extension K of Qp depends mostly on the discriminant of K, an extension containing less roots when it gets more ramified. We prove further that, for any positive integer r, a random p-adic polynomial of sufficiently large degree has about r roots on average in extensions of degree at most r.Beyond the mean, we also study higher moments and correlations between the number of roots in two given subsets of Qp (or, more generally, of a finite extension of Qp). In this perspective, we notably establish results highlighting that the roots tend to repel each other and quantify this phenomenon.
dc.description.sponsorshipCorrespondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
dc.language.isoen
dc.publisherCambridge University press
dc.subject.enrandom p-adic polynomials
dc.subject.enmass formula
dc.title.enWhere are the zeroes of a random p-adic polynomial?
dc.typeArticle de revue
dc.identifier.doi10.1017/fms.2022.27
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2110.03942
bordeaux.journalForum of Mathematics, Sigma
bordeaux.pagee55
bordeaux.volume10
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02557280
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02557280v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Forum%20of%20Mathematics,%20Sigma&rft.date=2022-07&rft.volume=10&rft.spage=e55&rft.epage=e55&rft.au=CARUSO,%20Xavier&rft.genre=article


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