Mathematician Gets out of prison

Weigh two of them against each other.If they balance, the third is counterfeit.If not, the lighter one is.Similarly, if the two sides balanced after your substitution,then one of the three plus coins you removed must be the heavier one.Weigh two of them against each other.If they balance, the third one is fake.If not, then it's the heavier one.The Emperor nods approvingly at your finding,and the counterfeiting Lord takes your place in the dungeon.