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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A lower bound for the class number of certain cubic number fields


Author: Günter Lettl
Journal: Math. Comp. 46 (1986), 659-666
MSC: Primary 11R16; Secondary 11R29
MathSciNet review: 829636
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Abstract: Let K be a cyclic number field with generating polynomial

$\displaystyle {X^3} - \frac{{a - 3}}{2}{X^2} - \frac{{a + 3}}{2}X - 1$

and conductor m. We will derive a lower bound for the class number of these fields and list all such fields with prime conductor $ m = ({a^2} + 27)/4$ or $ m = (1 + 27{b^2})/4$ and small class number.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0829636-1
PII: S 0025-5718(1986)0829636-1
Article copyright: © Copyright 1986 American Mathematical Society