Explicitly constructed extensions of the rational function field with prescribed splitting (Q1870032)

The author gives straightforward, explicit constructions, avoiding class field theory, for certain extensions of the rational function field \(\mathbb F_q(x)\). The techniques are based upon a use of ``\((n,q)\)-quasi-symmetric polynomials'': \( f(t) \in \mathbb F_q[t]\) such that \(f( \mathbb F_{q^n}) \subset \mathbb F_q\).