Purely cubic complex function fields with small units
Renate Scheidler · Acta Arithmetica · 2000
We investigate several infinite families of purely cubic complex congruence function fields with small fundamental units. Specifically, we compute the fundamental units of fields K of unit rank 1 and characteristic not equal to 3 where the generator of K over Fq(t) is a cube root of D = (M 3 − F)/E 3 with E 3 dividing M 3 − F and F dividing M 2. We also characterize all purely cubic complex function fields with regulator 1. 1