Whittaker rational structures and special values of the Asai 𝐿-function
Whittaker rational structures and special values of the Asai 𝐿-function
Let $F$ be a totally real number field and $E/F$ a totally imaginary quadratic extension of $F$. Let $\Pi$ be a cohomological, conjugate self-dual cuspidal automorphic representation of $GL_n(\mathbb A_E)$. Under a certain non-vanishing condition we relate the residue and the value of the Asai $L$-functions at $s=1$ with rational …