Whittaker rational structures and special values of the Asai $L$-function

@article{Grobner2014WhittakerRS,
  title={Whittaker rational structures and special values of the Asai \$L\$-function},
  author={Harald Grobner and Michael Harris and Erez Lapid},
  journal={arXiv: Number Theory},
  year={2014}
}
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 structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when $n = 2… 
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