Computation of real quadratic fields with class number one

Authors:
A. J. Stephens and H. C. Williams

Journal:
Math. Comp. **51** (1988), 809-824

MSC:
Primary 11R11; Secondary 11R29, 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-1988-0958644-7

MathSciNet review:
958644

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Abstract | References | Similar Articles | Additional Information

Abstract: A rapid method for determining whether the real quadratic field has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of and then uses the Generalized Riemann Hypothesis to rapidly estimate to the accuracy needed for determining whether or not the class number of is one. The results of running this algorithm on a computer for all prime values of *D* up to are also presented, together with further results on runs on intervals of size starting at .

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0958644-7

Article copyright:
© Copyright 1988
American Mathematical Society