On a quaternionic Picard theorem
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- by Cinzia Bisi and Jörg Winkelmann HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 7 (2020), 106-117
Abstract:
The classical theorem of Picard states that a non-constant holomorphic function $f:\mathbb {C}\to \mathbb {C}$ can avoid at most one value.
We investigate how many values a non-constant slice regular function of a quaternionic variable $f:\mathbb {H}\to \mathbb {H}$ may avoid.
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Additional Information
- Cinzia Bisi
- Affiliation: Department of Mathematics and Computer Sciences, Ferrara University, Via Machiavelli 30, 44121 Ferrara, Italy
- MR Author ID: 675004
- ORCID: 0000-0002-4973-1053
- Email: bsicnz@unife.it
- Jörg Winkelmann
- Affiliation: IB 3/111, Lehrstuhl Analysis II, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
- ORCID: 0000-0002-1781-5842
- Email: joerg.winkelmann@rub.de
- Received by editor(s): September 30, 2019
- Received by editor(s) in revised form: April 7, 2020, June 13, 2020, and June 24, 2020
- Published electronically: August 20, 2020
- Additional Notes: The two authors were partially supported by GNSAGA of INdAM. The first author was also partially supported by PRIN Varietá reali e complesse: geometria, topologia e analisi armonica.
- Communicated by: Filippo Bracci
- © Copyright 2020 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 7 (2020), 106-117
- MSC (2010): Primary 30G35
- DOI: https://doi.org/10.1090/bproc/54
- MathSciNet review: 4137036