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 the $ p$-part of the ideal class group of certain real abelian fields

Author: Hiroki Sumida-Takahashi
Journal: Math. Comp. 76 (2007), 1059-1071
MSC (2000): Primary 11R23, 11R70
Published electronically: January 5, 2007
MathSciNet review: 2291850
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Under Greenberg's conjecture, we give an efficient method to compute the $ p$-part of the ideal class group of certain real abelian fields by using cyclotomic units, Gauss sums and prime numbers. As numerical examples, we compute the $ p$-part of the ideal class group of the maximal real subfield of $ \mathbf{Q}(\sqrt{-f},\zeta_{p^{n+1}})$ in the range $ 1 <f<200$ and $ 5 \le p <100000$. In order to explain our method, we show an example whose ideal class group is not cyclic.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11R23, 11R70

Retrieve articles in all journals with MSC (2000): 11R23, 11R70

Additional Information

Hiroki Sumida-Takahashi
Affiliation: Faculty and School of Engineering, The University of Tokushima, 2-1 Minamijosanjima-cho, Tokushima 770-8506, Japan

PII: S 0025-5718(07)01926-6
Keywords: Ideal class group, Iwasawa invariant, abelian field, Greenberg's conjecture
Received by editor(s): September 7, 2005
Received by editor(s) in revised form: January 20, 2006
Published electronically: January 5, 2007
Additional Notes: This work was partially supported by the Grants-in-Aid for Encouragement of Young Scientists (No.\ 16740019) from Japan Society for the Promotion of Science.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.