Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect

Details Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect

2009-04-17

arxiv.org/abs/0904.2667v2

Annali di Matematica Pura ed Applicata, Online First, 11 August 2010

Mathematics

Complex Variables

Proof of Lemma 7 rewritten (thanks to an anonymous reviewer)

Scientific paper

10.1007/s10231-010-0162-1

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.

Affiliated with

Also associated with

No associations

Rating

Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-141104