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Trace forms of trinomials. (English) Zbl 0777.11010

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.

MSC:

11E12 Quadratic forms over global rings and fields
11E04 Quadratic forms over general fields
11E81 Algebraic theory of quadratic forms; Witt groups and rings
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