Divisorklassen der Ordnung \(\ell\) bei Kongruenzfunktionenkörpern
Let F be a function field of one variable over a finite field k. For a prime number \(\ell\) denote by \(C(F\cdot \bar k)(\ell)\) the group of divisor classes of order \(\ell\) which are defined over the algebraic closure \(\bar k\) of k. We give an upper bound B for the least number m such that \(C(F\cdot \bar k)(\ell)=C(F\cdot k_ m)(\ell)\) where \((k_ m:k)=m.\) B can be computed with the help of the zeta-function of F. [See also \textit{J. G. D'Mello} and \textit{M. L. Madan}, Manuscr. Math. 41, 75-107 (1983; Zbl 0516.12012)].
function field of one variable over a finite field
scientific article; zbMATH DE number 3857245