Are the Majus People of the Book, and who is their prophet?

Some scholars have held that the Majus (Zoroastrians) are People of the Book, citing as evidence that jizya was taken from them and that they had a revealed book that was lifted. However, they agreed on the prohibition of consuming their slaughtered animals and marrying their women, unlike the Jews and Christians. Ibn al-Qayyim, on the other hand, was of the view that the Majus are not People of the Book and never had a book, and that the taking of jizya from them does not validate them as People of the Book. His evidence for this is the Prophet's (peace be upon him) saying: "Treat them according to the Sunnah of the People of the Book," which indicates that they are not among them. Furthermore, the Qur'an does not mention any book or prophet for them, so their religion has no connection to the religions of the prophets.