Reducibility of polynomials $f(x,y)$ modulo $p$

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dc.creatorRuppert, Wolfgang M.
dc.date1998-08-05
dc.date.accessioned2026-07-07T05:25:37Z
dc.date.available2026-07-07T05:25:37Z
dc.descriptionWe consider absolutely irreducible polynomials $f \in Z[x,y]$ with $°_x(f)=m$, $°_y(f)=n$ and height $H$. We show that for any prime $p$ with $p>c_{mn} H^{2mn+n-1}$ the reduction $f \bmod p$ is also absolutely irreducible. Furthermore if the Bouniakowsky conjecture is true we show that there are infinitely many absolutely irreducible polynomials $f \in Z[x,y]$ which are reducible mod $p$ where $p$ is a prime with $p>H^{2m}$.
dc.descriptionLatex, 7 pages
dc.identifierhttps://arxiv.org/abs/math/9808021
dc.identifierhttp://arxiv.org/abs/math/9808021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77249
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleReducibility of polynomials $f(x,y)$ modulo $p$
dc.typetext

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