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.
Gentili, G., & Struppa, D.C. (2010). Regular functions on the space of Cayley numbers. Rocky Mountain Journal of Mathematics, 40(1), 225-241. doi: 10.1216/RMJ-2010-40-1-225
Rocky Mountain Mathematics Consortium