In recent history Harry Potter stories have been mentioned in other popular story series such as Doctor Who and The Simpsons.
Do any of the Harry Potter movies mention any other book or TV serials?
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While not a fictional series, there is a scene in Prisoner of Azkaban with a wizard doing wandless magic while reading A Brief History of Time by Stephen Hawking. The real life book is a treatise on quantum physics, and very well known. Introduction by Carl Sagan.
I can only recollect a mention of the fairy tales like "Cinderella" and few others in the Deathly Hallows when they are about to discuss The Tale of the Three Brothers when they visit Luna Lovegood's father at his home.