Some results concerning Voronoĭ's continued fraction over

Author:
H. C. Williams

Journal:
Math. Comp. **36** (1981), 631-652

MSC:
Primary 12A45

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606521-7

MathSciNet review:
606521

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Abstract: Let *D* be a cube-free integer and let be the fundamental unit of the pure cubic field . It is well known that Voronoi's algorithm can be used to determine . In this work several results concerning Voronoi's algorithm in are derived and it is shown how these results can be used to increase the speed of calculating for many values of *D*. Among these *D* values are those such that is not a prime and the class number of is not divisible by 3. A frequency table of all class numbers not divisible by 3 for all with is also presented.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0606521-7

Article copyright:
© Copyright 1981
American Mathematical Society