On the Computation of the Trace Form of Some Galois Extensions Original Research Article

We investigate the trace form trL/K : L → K : x maps to trL/Kx2of a finite Galois extensionL/K. In particular, we study 2-extensions of degree ≤ 16. Using some reduction theorems, these results yield a classification of nearly all trace forms of Galois extensions of degree ≤ 31. Finally, we study the trace form of a cyclotomic extension and of its maximal real subfield.