This analysis reveals that holomorphic functions are Nash if their real part is a Nash function, suggesting a strong connection between these mathematical constructs.
In this paper we show that a holomorphic function, defined on an open subset D of Cⁿ, is a complex Nash function if and only if its real part (or equivalently its imaginary part) is a real Nash function.
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Antonio Carbone (2025) studied this question.
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