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)

 

The determination of the imaginary abelian number fields with class number one


Author: Ken Yamamura
Journal: Math. Comp. 62 (1994), 899-921
MSC: Primary 11R20; Secondary 11R29
MathSciNet review: 1218347
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we determine all the imaginary abelian number fields with class number one. There exist exactly 172 imaginary abelian number fields with class number one. The maximal conductor of these fields is $ 10921 = 67 \cdot 163$, which is the conductor of the biquadratic number field $ {\mathbf{Q}}(\sqrt { - 67} ,\sqrt { - 163} )$.


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


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R20, 11R29

Retrieve articles in all journals with MSC: 11R20, 11R29


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1218347-3
PII: S 0025-5718(1994)1218347-3
Keywords: Imaginary abelian number fields, class number, characters
Article copyright: © Copyright 1994 American Mathematical Society