A numerical investigation into the length of the period of the continued fraction expansion of

Author:
H. C. Williams

Journal:
Math. Comp. **36** (1981), 593-601

MSC:
Primary 10A32; Secondary 10-04

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606518-7

MathSciNet review:
606518

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the length of the period of the continued fraction expansion of , where *D* is a positive square-free integer. In this paper it is suggested that and several tables of numerical results, which support this suggestion, are provided.

**[1]**B. D. Beach and H. C. Williams,*Some computer results on periodic continued fractions*, Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1971) Louisiana State Univ., Baton Rouge, La., 1971, pp. 133–146. MR**0321880****[2]**J. H. E. Cohn,*The length of the period of the simple continued fraction of 𝑑^{1/2}*, Pacific J. Math.**71**(1977), no. 1, 21–32. MR**0457335****[3]**Paul Lévy,*Sur le développement en fraction continue d’un nombre choisi au hasard*, Compositio Math.**3**(1936), 286–303 (French). MR**1556945****[4]**J. E. Littlewood, "On the class-number of the corpus ,"*Proc. London Math. Soc.*, v. 28, 1928, pp. 358-372.**[5]**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****[6]**Daniel Shanks,*Systematic examination of Littlewood’s bounds on 𝐿(1,𝜒)*, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 267–283. MR**0337827****[7]**Daniel Shanks,*The simplest cubic fields*, Math. Comp.**28**(1974), 1137–1152. MR**0352049**, https://doi.org/10.1090/S0025-5718-1974-0352049-8**[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****[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**, https://doi.org/10.1090/S0025-5718-1976-0414522-5

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606518-7

Article copyright:
© Copyright 1981
American Mathematical Society