The Zoroastrian prophecies predicted a new prophet, which would be heralded with certain signs in the sky. The three (?) wise men were the Zoroastrian priests who had read the signs correctly.
When the Jews were in captivity in Babylon, that region was undergoing an increasing influence of the Zoroastrian religion. This religion brought the goodness out of people, with one of its main tenets being to possess: “Good Thoughts, Good Words, Good Deeds.” The rulers, under this influence, decided to no longer keep the Jews in slavery. The Jewish religion, in turn, was also invigorated by Zoroastrianism: Judaism re-discovered the purpose religion. When the Jews returned to Israel, they were highly regarded amongst their neighbors for their honesty and advancing civilization. Socrates was influenced by this rising religion.
In a book called “Jesus”, one scholar posits that the time from when Jesus was 10 years old to 30 years old (the start of his ministry), Jesus and his family were in Babylon. Jesus was under the tutelage of the Zoroastrian faith. While he obviously did not become Zoroastrian himself, he brought back many of the Zoroastrian principles to Israel.