Trace forms of trinomials (Q1209598)

The trace forms of separable field extensions \(L/K\), \(\text{char}(K)\neq 2\), defined by trinomials \(X^ n+aX^ k+b\) are determined in the Witt ring of \(K\) (Theorem 1). In the case of an algebraic number field \(K\) a complete classification of all such trace forms defined by these trinomials is given (Theorem 2). This note generalizes the results of Serre for the case \(k=1\), Conner, Perlis for \(k=1\), \(n\) odd and \(K=\mathbb{Q}\) and Conner and Yui for some other special cases.