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A Lower Bound for the Class Number of Certain Cubic Number Fields

Gunter Lettl
1986 Mathematics of Computation  
Let AT be a cyclic number field with generating polynomial i a-3 ^ û + 3 x3 -Y-x1 -=~-x-i 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 = (a1 + 21)/A or m = (1 + 21b2)/A and small class number.
doi:10.2307/2008004 fatcat:ebtajmd4lvd3zfxkveqvdur5iq