Division-ample sets and the Diophantine problem for rings of integers

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dc.creatorCornelissen, Gunther
dc.creatorPheidas, Thanases
dc.creatorZahidi, Karim
dc.date2003-12-19
dc.date.accessioned2026-07-07T05:04:04Z
dc.date.available2026-07-07T05:04:04Z
dc.descriptionWe prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division-ample set of integers and of an elliptic curve of rank one over K). We relate division-ample sets to arithmetic of abelian varieties.
dc.description9 pages, uses a4paper, calrsfs
dc.identifierhttps://arxiv.org/abs/math/0312382
dc.identifierhttp://arxiv.org/abs/math/0312382
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69660
dc.subjectNumber Theory
dc.subjectLogic
dc.subject03B25, 11U05
dc.titleDivision-ample sets and the Diophantine problem for rings of integers
dc.typetext

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