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 der Kettenbruch-Entwicklung reeller Grössen*, Acta Math.**12**(1889), no. 1, 367–405 (German). MR**1554778**, https://doi.org/10.1007/BF02391885**[2]**B. MINNEGERODE, "Über eine neue Methode, die Pellshe Gleichung aufzulösen,"*Gött. Nachr.*, 1873, pp. 619-653.**[3]**Daniel Shanks,*The infrastructure of a real quadratic field and its applications*, Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972) Univ. Colorado, Boulder, Colo., 1972, pp. 217–224. MR**0389842****[4]**Daniel Shanks,*The simplest cubic fields*, Math. Comp.**28**(1974), 1137–1152. MR**0352049**, https://doi.org/10.1090/S0025-5718-1974-0352049-8**[5]**H. C. Williams and J. Broere,*A computational technique for evaluating 𝐿(1,𝜒) and the class number of a real quadratic field*, Math. Comp.**30**(1976), no. 136, 887–893. MR**0414522**, https://doi.org/10.1090/S0025-5718-1976-0414522-5**[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