Ring structure and the Fourier transform (Q1059676)

The authors give an interesting reworking of Schur's determination of the value of the Gaussian sum \(G=\sum_{a mod p}\exp (2\pi i a^ 2/p)\). Schur's proof comes from the observation that G is the trace of the finite Fourier transform on p points and is a beautiful example of the power of elementary linear algebra.