A comparison of automorphic \(L\)-functions in a theta series lifting for unitary groups
Let \(E/F\) be a quadratic extension of algebraic number fields. Consider the quasi-split unitary groups \(\text{U}(2n)\) and \(\text{U}(2n+1)\) over \(F\) split by \(E/F\). There is a \(\Theta\)-lifting \(\sigma\mapsto\sigma^{\ast}\) from cuspidal automorphic representations of \(\text{U}(2n)\) to automorphic representations of \(\text{U}(2n+1)\). The paper gives a relation between the partial \(L\)-functions \(L_S(s,\sigma\times\pi)\) and \(L_S(s,\sigma^{\ast}\times\pi)\), where \(\pi\) is an irreducible cuspidal automorphic representation of \(R_{E/F}\text{GL}(n)\).
scientific article; zbMATH DE number 1445776
scientific article