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Calculation of the regulator of $ {\bf Q}(\surd D)$ by use of the nearest integer continued fraction algorithm


Authors: H. C. Williams and P. A. Buhr
Journal: Math. Comp. 33 (1979), 369-381
MSC: Primary 12A25; Secondary 12A45
DOI: https://doi.org/10.1090/S0025-5718-1979-0514833-1
MathSciNet review: 514833
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Abstract: A computational method for determining the regulator of a real quadratic field $ Q(\sqrt D )$ is described. This method makes use of the properties of the nearest integer continued fraction of $ \sqrt D $ and is about 25


References [Enhancements On Off] (What's this?)

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  • [2] B. MINNEGERODE, "Über eine neue Methode, die Pellshe Gleichung aufzulösen," Gött. Nachr., 1873, pp. 619-653.
  • [3] D. SHANKS, "The infrastructure of a real quadratic field and its applications," Proceedings of the 1972 Number Theory Conference, Boulder, Colorado, 1972, pp. 217-224. MR 0389842 (52:10672)
  • [4] D. SHANKS, "Review of UMT File: Two related quadratic surds having continued fractions with exceptionally long periods," Math. Comp., v. 28, 1974, pp. 333-334. MR 0352049 (50:4537)
  • [5] H. C. WILLIAMS & J. BROERE, "A computational technique for evaluating $ L(1,\chi )$ and the class number of a real quadratic field," Math. Comp., v. 30, 1976, pp. 887-893. MR 0414522 (54:2623)
  • [6] H. C. WILLIAMS, "Some results concerning the nearest integer continued fraction expansion of $ \sqrt D $," J. Reine Angew. Math. (To appear.)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0514833-1
Article copyright: © Copyright 1979 American Mathematical Society

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