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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/19.4.329
- Publisher site
- See Article on Publisher Site
Abstract
We prove that the zero set of any quaternionic (or octonionic) analytic function f with central (that is, real) coefficients is the disjoint union of codimension two spheres in R4 or R8 (respectively) and certain purely real points. In particular, for polynomials with real coefficients, the complete root‐set is geometrically characterisable from the lay‐out of the roots in the complex plane. The root‐set becomes the union of a finite number of codimension 2 Euclidean spheres together with a finite number of real points. We also find the preimages f−1 for any quaternion (or octonion) A.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 1987