A computational technique for evaluating and the class number of a real quadratic field

Authors:
H. C. Williams and J. Broere

Journal:
Math. Comp. **30** (1976), 887-893

MSC:
Primary 12A70; Secondary 12-04

DOI:
https://doi.org/10.1090/S0025-5718-1976-0414522-5

MathSciNet review:
0414522

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Abstract: A description is given of a method for estimating to sufficient accuracy to determine the class number of a real quadratic field. This algorithm was implemented on an IBM/370-158 computer and the class number, regulator, and value of were obtained for each real quadratic field . Several tables, summarizing various results of these computations, are also presented.

**[1]**Pierre Barrucand,*Sur certaines séries de Dirichlet*, C. R. Acad. Sci. Paris Sér. A-B**269**(1969), A294–A296 (French). MR**0246832****[2]**M. D. Hendy,*The distribution of ideal class numbers of real quadratic fields*, Math. Comp.**29**(1975), no. 132, 1129–1134. MR**0409402**, https://doi.org/10.1090/S0025-5718-1975-0409402-4**[3]**E. L. INCE, "Cycles of reduced ideals in quadratic fields,"*Mathematical Tables*, vol. IV, British Association for the Advancement of Science, London, 1934.**[4]**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****[5]**H. J. S. SMITH, "Note on the theory of the Pellian equation and of binary quadratic forms of a positive discriminant,"*Proc. London Math. Soc.*, v. 7, 1875/76, pp. 199-208.

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0414522-5

Article copyright:
© Copyright 1976
American Mathematical Society