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

Lettl, Günter

doi:10.1090/S0025-5718-1986-0829636-1

A lower bound for the class number of certain cubic number fields
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Math. Comp. 46 (1986), 659-666 Request permission

Abstract:

Let K be a cyclic number field with generating polynomial \[ {X^3} - \frac {{a - 3}}{2}{X^2} - \frac {{a + 3}}{2}X - 1\] 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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