Cyclotomic function fields with divisor class number one
Let \(k\) denote the rational function field over any finite field \(F\). For any non-constant polynomial \(M\) over \(F\), the authors define the cyclotomic function field \(K_ M\), an extension of \(k\), after \textit{S. Galovich} and \textit{M. Rosen} [J. Number Theory 13, 363--375 (1981; Zbl 0473.12014)]. They obtain formulae for the genera of \(K_ M\) and of its ``maximal real subfield'' \(K_ M^+\) and apply them to determine all fields \(K_ M\) and \(K_ M^+\) with class number one. A complete list of the fields \(K_ M\) and \(K_ M^+\) with genus one is also given.
scientific article; zbMATH DE number 4214148