Abstract
We investigate the trace form trL/K:L→K:x↦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.
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