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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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In case you haven't heard about it, the book "The Theory of Irrationalities of the Third Degree" by B. N. Delone and D. K. Faddeev (Volume 10 of Translations of Mathematical Monographs, AMS). It contains a lot of information on Voronoi's results. In any case, I'm also interested in a translation of the thesis :) –  felix Nov 19 '10 at 5:17

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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 e-mail it to you. E-mail me, contact details at www.math.ucalgary.ca/~rscheidl.

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Sounds like the book is very rare. I checked Google Books and could not find it. You might want to post the full details and the ISBN number of the book, so everyone can look it up on the WorldCat. However, if it is as rare as it seems it is, and you are going to scan it anyway, you might want to do a public service and post it on your webpage. If you suddenly get cease and desist letter from the copyright owner, you will have to take it down, but until then... –  Igor Pak Dec 5 '10 at 11:18

"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/

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Thank you, but I specifically want Voronoi's dissertation. –  Michael Nov 21 '10 at 7:22

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.

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Can you say anything about your reasons? In our group we use Voronoi's algorithms for studying statistical and extrimal properties of lattices. –  Alexey Ustinov Dec 5 '10 at 12:06

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