# English translation of Voronoy paper on generalized Pell's equation

I'm not sure if this is the proper place to ask this, but I am looking for an English translation of Voronoy's paper on the generalized Pell's equation. It might be his doctoral dissertation; I'm not sure. I believe the title is "On a generalization of the Algorithm of Continued Fractions".

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If you seek a detailed exposition of Voronoi's algorithm then see below. Based on what they wrote, the authors may have an English translation of some of his work.

Calculation of the Regulator of a Pure Cubic Field

By H. C. Williams, G. Cormack and E. Seah
Mathematics of Computation, Vol. 34, No. 150 (Apr., 1980), pp. 567-6

Abstract. A description is given of a modified version of Voronoi's algorithm for obtaining the regulator of a pure cubic field $\mathbb Q(\sqrt[3]{D})$. This new algorithm has the advantage of executing relatively rapidly for large values of $D$. It also eliminates a computational problem which occurs in almost all algorithms for finding units in algebraic number fields. This is the problem of performing calculations involving algebraic irrationals by using only approximations of these numbers.

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Here is the freely accessible version from AMS. – J. M. Nov 19 '10 at 6:14
Thank you, Bill. I have found a few papers that detail Voronoi's algorithm, but they all reference his paper in Russian (as does this one). Would you recommend contacting the paper's authors to see if they have English translations? – James Nov 19 '10 at 6:38
Yes, do try Hugh Williams math.ucalgary.ca/profiles/hugh-williams – Bill Dubuque Nov 19 '10 at 6:53