Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



A rigorous subexponential algorithm for computation of class groups

Authors: James L. Hafner and Kevin S. McCurley
Journal: J. Amer. Math. Soc. 2 (1989), 837-850
MSC: Primary 11Y40; Secondary 11R29
MathSciNet review: 1002631
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $C( - d)$ denote the Gauss Class Group of quadratic forms of a negative discriminant $- d$ (or equivalently, the class group of the imaginary quadratic field $Q(\sqrt { - d} )$). We give a rigorous proof that there exists a Las Vegas algorithm that will compute the structure of $C( - d)$ with an expected running time of $L{(d)^{\sqrt 2 + o(1)}}$ bit operations, where $L(d) = {\text {exp}}(\sqrt {\log d\;\log \log d} )$. Thus, of course, also includes the computation of the class number $h( - d)$, the cardinality of $C( - d)$.

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

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 11Y40, 11R29

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

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society