We employ tools from complex analysis to construct the ∗-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the ∗-exponential; we establish sufficient conditions for the ∗-product of two ∗-exponentials to also be a ∗-exponential; we calculate the slice derivative of the ∗-exponential of a regular function.
Altavilla, A., Mongodi, S. (2025). The ∗-Exponential as a Covering Map. COMPUTATIONAL METHODS AND FUNCTION THEORY, 25(4 (December 2025)), 801-829 [10.1007/s40315-024-00558-z].
The ∗-Exponential as a Covering Map
Mongodi S.
2025
Abstract
We employ tools from complex analysis to construct the ∗-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the ∗-exponential; we establish sufficient conditions for the ∗-product of two ∗-exponentials to also be a ∗-exponential; we calculate the slice derivative of the ∗-exponential of a regular function.
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