(This question was posted on math.stackexchange a week ago at http://math.stackexchange.com/questions/187315/definitive-source-about-dirichlet-finally-proving-the-unit-theorem-in-the-sistinbut and still has received no answers there, so I hope it's okay to post it here too.)
In a few books or survey articles (e.g., page 49 of Helmut Koch's "Number Theory: Algebraic Numbers and Algebraic Functions") it is said that Dirichlet figured out a proof of the unit theorem while listening to an Easter concert in the Sistine Chapel. My question is: what is the evidence for this story?
From an internet search I found that Kummer wrote on p. 343 of volume 2 of Dirichlet's collected works that Dirichlet could work on math in all kinds of situations, and then Kummer says "Als Beispiel hierfür kann ich anführen, dass er die Lösung eines schwierigen Problems der Zahlentheorie, womit er sich längere Zeit vergeblich bemüht hatte, in der Sixtinischen Kapelle in Rom ergründet hat, während des Anhörens der Ostermusik, die in derselben aufgeführt zu werden pflegt" (translation: "As an example I can say that he found the solution to a difficult problem in number theory, which he had worked on for a considerable amount of time without success, in the Sistine Chapel in Rome while he was listening to the Easter music that tends to be played there.")
Notice Kummer does not say precisely what the "difficult problem" was. Maybe it is just an oral tradition that the problem is the unit theorem, but I would like a more definitive source.
I don't read German well, but if you do then Kummer's essay on Dirichlet can be read online. It starts on http://archive.org/stream/glejeunedirichl00dirigoog#page/n323/mode/1up and page 343 is http://archive.org/stream/glejeunedirichl00dirigoog#page/n355/mode/1up.