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There is a remark one can find in various books or survey articles (e.g., page 49 of Helmut Koch's "Number Theory: Algebraic Numbers and Algebraic Functions") saying 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?

Today I did an internet search and 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.

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    Helmut Koch's email address is available [here](http://www.bbaw.de/die-akademie/mitglieder/712). Koch is also the author of Dirichlet's entry on [this page](http://www.bbaw.de/die-akademie/akademiegeschichte/historischer-kalender/februar) (giving the year 1844 as further information). Elstrodt's [biographical sketch](http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf) of Dirichlet also contains the episode and cites work of Dirichlet's student Bachmann [Ba.1] and [Ba.2] that might contain further pointers.2012-08-27
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    OK, I wrote to Koch and Elstrodt. The paper [Ba.2] by Bachmann is in Crelle (vol. 67, pp. 200--204) and mentions nothing as it is purely a research article.2012-08-27
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    The question was [posted on MO](http://mathoverflow.net/questions/106196/).2012-09-03
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    You might want to repost this at [History of Science and Mathematics Stack Exchange](http://hsm.stackexchange.com/).2016-09-01

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