A simple generalization of analytic function theory (Q1113325)

The author develops an interesting function theory over \(R^ t\), using the cyclic algebra with base \(1,j,...,j^ t=-1\). Important is the representation by skew circulix matrices which have been used in number theory by the author [Fibonacci Q. 24, 47-60, 176-177 (1986; Zbl 0599.10009 and Zbl 0599.10010)]. The following subjects are dealt with: generalized trigonometry, generalized Cauchy Riemann equations, examples of analytic functions within the theory, Cauchy's theorem, an interesting special form of Cauchy's integral formula, maximum modulus theorem, Cauchy's inequality and Liouville's theorem.