We study two criterions of cyclicity for divisor class groups of functions fields, the first one involves Artin L-functions and the second one involves "affine" class groups. We show that, in general, these two criterions are not linked.
Artin automorphisms, Cyclotomic function fields, and Folded list-decodable codes
Cyclotomic function fields over finite fields with irreducible quadratic modulus
The divisibility of zeta functions of cyclotomic function fields
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