The Simplest Cubic Fields
- 1 October 1974
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 28 (128) , 1137-1152
- https://doi.org/10.2307/2005372
Abstract
The cyclic cubic fields generated by ${x^3} = a{x^2} + (a + 3)x + 1$ are studied in detail. The regulators are relatively small and are known at once. The class numbers are always of the form ${A^2} + 3{B^2}$, are relatively large and easy to compute. The class groups are usually easy to determine since one has the theorem that if m is divisible only by ${\text {primes}} \equiv 2\pmod 3$, then the m-rank of the class group is even. Fields with different 3-ranks are treated separately.
Keywords
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