A computational technique for evaluating 𝐿(1,𝜒) and the class number of a real quadratic field

Williams, H. C.; Broere, J.

doi:10.1090/S0025-5718-1976-0414522-5

A computational technique for evaluating $L(1,\chi )$ and the class number of a real quadratic field
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by H. C. Williams and J. Broere PDF

Math. Comp. 30 (1976), 887-893 Request permission

Abstract:

A description is given of a method for estimating $L(1,\chi )$ 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 $L(1,\chi )$ were obtained for each real quadratic field $Q(\sqrt D )\;(D = 2,3, \ldots ,149999)$. Several tables, summarizing various results of these computations, are also presented.

References

Pierre Barrucand, Sur certaines séries de Dirichlet, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A294–A296 (French). MR 246832
M. D. Hendy, The distribution of ideal class numbers of real quadratic fields, Math. Comp. 29 (1975), no. 132, 1129–1134. MR 409402, DOI 10.1090/S0025-5718-1975-0409402-4

Mathematical Tables

Daniel Shanks, Systematic examination of Littlewood’s bounds on $L(1,\,\chi )$, 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

Proc. London Math. Soc.