The residual spectrum of \(Sp(2)\) (Q1340373)

Let \(G\) be the rank two symplectic group \(\text{Sp} (2)\) over a number field \(k\), and let \(A\) be the adele ring of \(k\). The space of \(L^2\) automorphic forms on \(G(k) \setminus G(A)\) decomposes into a direct sum of the discrete spectrum \(L^2_{\text{disc}}\) and the continuous spectrum \(L^2_{\text{const}}\). The cuspidal spectrum \(L^2_{\text{cusp}}\) is contained in \(L^2_{\text{disc}}\). The orthogonal complement of the cuspidal spectrum in the discrete spectrum is called the residual spectrum. The author obtains the irreducible decomposition of the residual spectrum when \(k\) is totally real.