While there is abundant literature available on value distribution of meromorphic functions, I am interested to know whether the value distribution theory for bicomplex meromorphic functions has been studied or not. I couldn't find any references for the same.
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$\begingroup$ Can you please define what you mean by a bicomplex meromorphic function? Is it a meromorphic function of two complex variables? Or do you mean meromorphic functions over the bicomplex numbers? $\endgroup$– M.G.Commented Apr 7, 2022 at 13:11
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1$\begingroup$ By bicomplex meromorphic functions, I mean functions meromorphic over bicomplex numbers $\endgroup$– NikCommented Apr 7, 2022 at 15:02
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$\begingroup$ Ok, I see. I am afraid they are not very interesting (see my answer), which is probably why you don't find anything about them. $\endgroup$– M.G.Commented Apr 7, 2022 at 15:41
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1 Answer
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Since the bicomplex numbers are isomorphic to $\mathbb{C} \oplus \mathbb{C}$ as a $\mathbb{C}$-algebra, it is not too difficult to see that (after a linear change of coordinates) any bicomplex-holomorphic function is of the form $(f(z),g(w))$ with $f$ and $g$ being ordinary holomorphic functions. So, the behavior of bicomplex-meromorphic functions (in any suitable sense) is just a corollary of that of ordinary meromorphic functions.
