Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 958644
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A rapid method for determining whether the real quadratic field $ \mathcal{K} = \mathcal{Q}(\sqrt D )$ has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of $ \mathcal{K}$ and then uses the Generalized Riemann Hypothesis to rapidly estimate $ L(1,\chi )$ to the accuracy needed for determining whether or not the class number of $ \mathcal{K}$ is one. The results of running this algorithm on a computer for all prime values of D up to $ {10^9}$ are also presented, together with further results on runs on intervals of size $ {10^7}$ starting at $ {10^i}\,(i = 9,10, \ldots ,16)$.


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


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R11, 11R29, 11Y40

Retrieve articles in all journals with MSC: 11R11, 11R29, 11Y40


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1988-0958644-7
PII: S 0025-5718(1988)0958644-7
Article copyright: © Copyright 1988 American Mathematical Society