Cuspidal part of an Eisenstein series restricted to an index 2 subfield

Yueke Hu

Let $\mathbb{E}$ be a quadratic extension of a number field $\mathbb{F}$. Let $E(g,s)$ be an Eisenstein series on $G{L}_2(\mathbb{E})$, and let $F$ be a cuspidal automorphic form on…