I am looking for an English translation of Voronoi's doctoral dissertation, "On a generalization of the Algorithm of Continued Fractions." I can only find it in the original Russian.
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Hi Michael and Joel: there is in fact an English translation of Voronoi's thesis by Emma Lehmer. I have it in printed form. I can have it scanned as PDF and email it to you. Email me, contact details at www.math.ucalgary.ca/~rscheidl. 


"The Theory of Irrationalities of the Third Degree" is much more clere than original Voronoi's doctoral dissertation. There are some recent works on Voronoi's and Minkowski's algoritms. You can start for example from http://www.springerlink.com/content/g364t1u85r103584/ 


Hi Michael, I've been looking for the dissertation too, and probably for the same reason you are. I honestly don't think it has been translated into English. 

