A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras

Abstract

Let K be a field with characteristic different from 2 and let S be a symbol algebra over K. We compute the symmetric powers of hyperbolic quadratic forms over K. Also, we compute the symmetric powers of the quadratic trace form of S. In both cases, we apply a generalized form of the Vandermonde convolution in the course of the computations.