Calculation of the regulator of 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 is described. This method makes use of the properties of the nearest integer continued fraction of and is about 25

**[1]**A. HURWITZ, "Über eine besondere Art die Kettenbruchentwicklung reeller Grössen,"*Acta Math.*, v. 12, 1889, pp. 367-405. MR**1554778****[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 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 ,"*J. Reine Angew. Math.*(To appear.)

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514833-1

Article copyright:
© Copyright 1979
American Mathematical Society