MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
show/hide this revision's text 1 [made Community Wiki]

This should be a comment in regards to the answer of A One-Sentence Proof That Every Prime p≡1(mod4) Is a Sum of Two Squares D. Zagier , but I don't have the reputation. While it isn't the actual paper, there is a short but interesting note that goes through how such an involution is constructed in the first result of a google search here.