Let $\Re$ denote real part and $|\cdot|$ absolute value.
Does there exist, for every entire $f$, an entire $g$ such that $\Re f = \ln |g|$ ?
2026-04-03 06:08:59.1775196539
Can one realize the real part of every entire function $f$ as $\ln| g|$ with $g$ entire?
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How about the function $g(z)=e^{f(z)}$?