A numerical investigation into the length of the period of the continued fraction expansion of
Author:
H. C. Williams
Journal:
Math. Comp. 36 (1981), 593601
MSC:
Primary 10A32; Secondary 1004
MathSciNet review:
606518
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Abstract 
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Abstract: Let be the length of the period of the continued fraction expansion of , where D is a positive squarefree integer. In this paper it is suggested that and several tables of numerical results, which support this suggestion, are provided.
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 [6]
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 [8]
R.
G. Stanton, C.
Sudler Jr., and H.
C. Williams, An upper bound for the period of the simple continued
fraction for √𝐷, Pacific J. Math. 67
(1976), no. 2, 525–536. MR 0429724
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 [9]
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
(54 #2623), http://dx.doi.org/10.1090/S00255718197604145225
 [1]
 B. D. Beach & H. C. Williams, "Some computer results on periodic continued fractions," Proc. Second Louisiana Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, La., 1971, pp. 133146. MR 0321880 (48:245)
 [2]
 J. H. E. Cohn, "The length of the period of the simple continued fraction of ," Pacific J. Math., v. 71, 1977, pp. 2132. MR 0457335 (56:15543)
 [3]
 Paul Lévy, "Sur le développement en fraction continue d'un nombre choisi au hasard," Compositio Math., v. 3, 1936, pp. 286303. MR 1556945
 [4]
 J. E. Littlewood, "On the classnumber of the corpus ," Proc. London Math. Soc., v. 28, 1928, pp. 358372.
 [5]
 Daniel Shanks, "The infrastructure of a real quadratic field and its applications," Proc. Boulder Symposium, August 1972, Univ. of Colorado, Boulder, 1972, pp. 217224. MR 0389842 (52:10672)
 [6]
 Daniel Shanks, Systematic Examination of Littlewood's Bounds on , Proc. Sympos. Pure Math., Vol. 24, Amer. Math. Soc., Providence, R.I., 1973, pp. 267  283. MR 0337827 (49:2596)
 [7]
 Daniel Shanks, "Review of UMT File: Two related quadratic surds having continued fractions with exceptionally long periods," Math. Comp., v. 28, 1974, pp. 333334. MR 0352049 (50:4537)
 [8]
 R. G. Stanton, G. Sudler, Jr. & H. C. Williams, "An upper bound for the period of the simple continued fraction for ," Pacific J. Math., v. 67, 1976, pp. 525536. MR 0429724 (55:2735)
 [9]
 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. 887893. MR 0414522 (54:2623)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106065187
PII:
S 00255718(1981)06065187
Article copyright:
© Copyright 1981
American Mathematical Society
