adic computation of real quadratic class numbers
Authors:
J. Buchmann, J. W. Sands and H. C. Williams
Journal:
Math. Comp. 54 (1990), 855868
MSC:
Primary 11Y40; Secondary 11R29
MathSciNet review:
1010596
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Abstract: Let be any real quadratic field and let be the class number of . A method utilizing the padic class number formula for is described for evaluating . The technique was programmed for a micro VAX II computer and run on all fields with radicand .
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 Y. Amice and J. Fresnel, Fonctions zêta padiques des corps de nombres abeliens réels, Acta Arith. 20 (1972), 353384. MR 0337898 (49:2667)
 [2]
 J. W. L. Glaisher, Residue of the product of p numbers in arithmetical progression mod and , Messenger Math. 30 (190001), 7192.
 [3]
 H. W. Leopoldt, Eine padische Theorie der Zetawerte. II, Die padische TTransformation, J. Reine Angew. Math. 274/275 (1975), 224239. MR 0379446 (52:351)
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 R. A. Mollin and H. C. Williams, Computation of the class number of a real quadratic field, Advances in the Theory of Computation and Computational Mathematics (to appear). MR 1162532 (93d:11134)
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 I. S. Slavutskii, Upper bounds and numerical calculation of the number of ideal classes of real quadratic fields, Amer. Math. Soc. Transl. (2) 82 (1969), 6772.
 [6]
 R. G. Stanton, C. Sudler, Jr., and H. C. Williams, An upper bound for the period of the simple continued fraction for , Pacific J. Math. 67 (1976), 525536. MR 0429724 (55:2735)
 [7]
 A. J. Stephens and H. C. Williams, Some computational results on a problem concerning powerful numbers, Math. Comp. 50 (1988), 619632. MR 929558 (89d:11091)
 [8]
 H. Wada, A table of ideal class numbers of real quadratic fields, Kôkyûroku in Math., no. 10, Sophia University, Tokyo, 1981.
 [9]
 L. C. Washington, Introduction to cyclotomic fields, SpringerVerlag, New York, 1982. MR 718674 (85g:11001)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199010105969
PII:
S 00255718(1990)10105969
Article copyright:
© Copyright 1990
American Mathematical Society
