A novel operation associated with Gauss' arithmetic-geometric means

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dc.creatorTanimoto, Shinji
dc.date2007-08-27
dc.date.accessioned2026-07-07T08:25:48Z
dc.date.available2026-07-07T08:25:48Z
dc.descriptionThe arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an arithmetic operation such that AGM is the mean for this operation, it can be regarded as an intermediate operation between addition and multiplication in view of the meaning of AGM. In this paper such an operation is introduced and several of its algebraic properties are proved.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/0708.3521
dc.identifierhttp://arxiv.org/abs/0708.3521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136742
dc.subjectNumber Theory
dc.subjectGeneral Mathematics
dc.subject11A99
dc.titleA novel operation associated with Gauss' arithmetic-geometric means
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