Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect
Complex Variables
2010-08-26 v2 Rings and Algebras
Abstract
We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of their product. In the case of octonionic polynomials, we get a strong form of the fundamental theorem of algebra. We prove that the sum of the multiplicities of zeros equals the degree of the polynomial and obtain a factorization in linear polynomials.
Cite
@article{arxiv.0904.2667,
title = {Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect},
author = {Riccardo Ghiloni and Alessandro Perotti},
journal= {arXiv preprint arXiv:0904.2667},
year = {2010}
}
Comments
Proof of Lemma 7 rewritten (thanks to an anonymous reviewer)