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

DOI10.1007/s10231-010-0162-1zbMath1246.30013arXiv0904.2667OpenAlexW3100358902WikidataQ125021898 ScholiaQ125021898MaRDI QIDQ642110

Riccardo Ghiloni, Alessandro Perotti

Publication date: 25 October 2011

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.2667

zbMATH Keywords

quaternionsfundamental theorem of algebraoctonionsfunctions of a hypercomplex variable

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Other generalizations of function theory of one complex variable (32A30)

Related Items (20)

Growth and distortion theorems for slice monogenic functions ⋮ Schauder bases in Dirac modules over quaternions ⋮ Singularities of slice regular functions over real alternative \(^{\ast}\)-algebras ⋮ Slice conformality and Riemann manifolds on quaternions and octonions ⋮ Slice Fueter-regular functions ⋮ Zeros, factorizations and least common multiples of quaternion polynomials ⋮ Slice regular functions on real alternative algebras ⋮ Differential topological aspects in octonionic monogenic function theory ⋮ Vieta's formulae for regular polynomials of a quaternionic variable ⋮ The algebra of slice functions ⋮ A new series expansion for slice regular functions ⋮ Slice Dirac operator over octonions ⋮ On a class of right linearly differentiable functions of Cayley-Dickson variables ⋮ Division algebras of slice functions ⋮ Slice Regular Functions on Regular Quadratic Cones of Real Alternative Algebras ⋮ On geometric aspects of quaternionic and octonionic slice regular functions ⋮ ON THE CLASSIFICATION OF CENTRALLY FINITE ALTERNATIVE DIVISION RINGS SATISFYING ALGEBRAIC CLOSURE CONDITIONS ⋮ Regular functions on the space of Cayley numbers ⋮ Cauchy kernel of slice Dirac operator in octonions with complex spine ⋮ Slice regular functions and orthogonal complex structures over \(\mathbb{R}^8\)

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