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Jan 11 at 11:36 comment added Jens Fischer Yes, but the degree condition does not work because for constant functions thz degree of $P$ and $Q$ are identical.
Jan 11 at 11:11 comment added Mariano Suárez-Álvarez The constant functions are meromorphic and all their poles, of which there are finitely many, are on the unit circle.
Jan 11 at 10:50 history edited Jens Fischer CC BY-SA 4.0
Power of the polynomial $Q$ was in the wrong place.
Jan 11 at 9:28 history asked Jens Fischer CC BY-SA 4.0