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A computational technique for evaluating $ L(1,\chi )$ 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 | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] PIERRE A. BARRUCAND, "Sur certaines séries de Dirichlet," C. R. Acad. Sci Paris Sér. A-B, v. 269, 1969, A294-A296. MR 40 # 101. MR 0246832 (40:101)
  • [2] M. D. HENDY, "The distribution of ideal class numbers of real quadratic fields," Math. Comp., v. 29, 1975, pp. 1129-1134. MR 0409402 (53:13157)
  • [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,\chi )$, Proc. Sympos. Pure Math., vol. 24, Amer. Math. Soc., Providence, R.I., 1973, pp. 267-283. MR 49 #2596. MR 0337827 (49:2596)
  • [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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1976-0414522-5
Article copyright: © Copyright 1976 American Mathematical Society

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