Ghiloni, Riccardo and Perotti, Alessandro (2010) *Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect.* In «Annali di Matematica Pura ed Applicata», Springer Verlag. ISBN 0373-3114 (In Press)

## Abstract

We study in detail the zero set of a slice 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. The original publication is available at www.springerlink.com

Item Type: | Article in journal |

Department or Research center: | Mathematics |

Subjects: | Q Science > QA Mathematics > QA299.6 Analysis |

Uncontrolled Keywords: | Quaternions, Octonions, Functions of hypercomplex variable, Fundamental theorem of algebra |

Repository staff approval on: | 13 Jan 2011 |
---|

### Actions (login required)