Arithmetic Laplacians

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dc.creatorBuium, Alexandru
dc.creatorSimanca, Santiago R.
dc.date2008-05-02
dc.date.accessioned2026-07-07T09:36:40Z
dc.date.available2026-07-07T09:36:40Z
dc.descriptionWe develop an arithmetic analogue of elliptic partial differential equations. The role of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat quotient operators subjected to certain commutation relations. This leads to arithmetic linear partial differential equations on algebraic groups that are analogues of certain operators in analysis constructed from Laplacians. We classify all such equations on one dimensional groups, and analyze their spaces of solutions.
dc.identifierhttps://arxiv.org/abs/0805.0256
dc.identifierhttp://arxiv.org/abs/0805.0256
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160200
dc.subjectNumber Theory
dc.subjectAnalysis of PDEs
dc.subject11G07; 35J99
dc.titleArithmetic Laplacians
dc.typetext

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