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In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.


This article was originally published in Rocky Mountain Journal of Mathematics, volume 40, issue 1, in 2010. DOI: 10.1216/RMJ-2010-40-1-225

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Rocky Mountain Mathematics Consortium



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