Rupert Pupkin’s mother dead or alive?

Something that has always perplexed me about “The King of Comedy” is the character of Rupert Pupkin’s mother. Early in the film she vexes Rupert with her interruptions while he is indulging his fantasies of talk show stardom. Then when he is finally allowed to perform his comedy routine on television, he claims that his mother is deceased. What is the truth?

Given Rupert’s fragile mental condition, my first guess would be that his mother is indeed dead, and that her voice and fleeting image are hallucinations. Then again, Rupert is an opportunist and would likely not hesitate to lie in order to enhance his material, even at his mother’s expense.

Obviously it is meant to be ambiguous but I would still like to know what others think.