Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Quadratic class numbers and character sums

Author: Andrew R. Booker
Journal: Math. Comp. 75 (2006), 1481-1492
MSC (2000): Primary 11Y35
Published electronically: March 21, 2006
MathSciNet review: 2219039
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present an algorithm for computing the class number of the quadratic number field of discriminant $ d$. The algorithm terminates unconditionally with the correct answer and, under the GRH, executes in $ O_{\varepsilon}(\vert d\vert^{1/4+\varepsilon})$ steps. The technique used combines algebraic methods with Burgess' theorem on character sums to estimate $ L(1,\chi_d)$. We give an explicit version of Burgess' theorem valid for prime discriminants and, as an application, we compute the class number of a 32-digit discriminant.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11Y35

Retrieve articles in all journals with MSC (2000): 11Y35

Additional Information

Andrew R. Booker
Affiliation: Department of Mathematics, 530 Church Street, University of Michigan, Ann Arbor, Michigan 48109

Received by editor(s): November 26, 2004
Received by editor(s) in revised form: July 21, 2005
Published electronically: March 21, 2006
Additional Notes: The author was supported by an NSF postdoctoral fellowship
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.