Spade:
In light of the posts that over-complicate something relatively simple; the information source for 537 as the date which Cyrus the Great decreed that the Israelites could return to Judea came from the Bible and Brown University Studies, Vol. XIX, Babylonian Chronology 626 B.C.-A.D. 75, (1956) Parker and Dubberstein.
The Bible says Cyrus made the decree "in the first year" (Ezr. 1:1). PD's Babylonian Chronology has Cyrus' first year running from Spring 538 BCE to Spring 537 BCE. So at some point between Spring 538 and Spring 537 (and the Bible doesn't tell us at which point that was), Cyrus made his decree. It MAY have been toward the end of his first year in Spring 537, but equally it could have been early in his first year - Spring 538. So conceivably, the Jews could have been settled in their home towns by the Fall of 538. In fact, seeing as there is no mention of Cyrus having clocked up another regnal year since the decree in Ezr. 1:1 and the month when the exiles were settled in 3:1, the argument for a 538 return is stronger.
Of course, all this assumes Ezra was counting regnal years the same as the Babylonians. If not, it's another story and the 'relatively simple' again becomes a little more complicated.
The only scholarly study that challenges some aspects of these secular sources is "Assyrian, Babylonian, Egyptian and Persian Chronology Compared with the Chronology of the Bible volume I Persian Chronology and the Length of the Babylonian Exile of the Jews" from Rolf Furuli.
Unfortunately, it didn't turn out to be a serious challenge. The faulty premises and data he used led to faulty conclusions.
The reason Charles Taze Russel and his associates came to a conclusion about Bible prophecy regarding the "appointed time of the nations" was to understand when Jehovah will intervene of behalf of humanity. If all the facts are obscured to the point to where no conclusions can be reached, divine prophecy is an utter failure on God's behalf, not its interpreters.
And CTR and his associates were wrong. Jehovah didn't intervene on behalf of humanity in 1914 or thereabouts. And modern JWs are in the same position now - not knowing when Jehovah will intervene on behalf of humanity. All they believe, and have believed for the best part of a century, is that He will somehow act 'soon.'
The Bible is crystal clear when iterating prophetic words in which sound conclusions can be reached. A matrix of data can often be used to obscure clear instruction, but that's not the way God operates, that's the way some humans operate.
If Bible prophecy is crystal clear, sound conclusions would have been reached centuries ago. As it is, humans keep concluding wrongly about when God is going to act. That's why Jesus himself told humans to NOT to try and second-guess God's timetable! When humans try to second-guess God's timetable, they become the ones over-complicating and obscuring the relatively simple gospel message.
*waves at Lars* - Ahh, I guess you're doing the rounds and it's JWN's turn again LOL.