On binary quadratic forms with semigroup property

dc.creatorAicardi, Francesca
dc.creatorTimorin, Vladlen
dc.date2004-12-07
dc.date2005-11-18
dc.date.accessioned2026-07-07T06:39:08Z
dc.date.available2026-07-07T06:39:08Z
dc.descriptionA quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If there is an integer bilinear map s such that f(s(x,y))=f(x)f(y) for all vectors x and y from the integer 2-dimensional lattice, then the form f has semigroup property. We give an explicit description of all pairs (f,s) with the property stated above. We do not know any other examples of forms with semigroup property.
dc.descriptionv3: minor changes, referenced added; 28 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0412145
dc.identifierhttp://arxiv.org/abs/math/0412145
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100971
dc.subjectNumber Theory
dc.subject11E16; 11E41
dc.titleOn binary quadratic forms with semigroup property
dc.typetext

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