On the special values of automorphic \(L\)-functions (Q1876846)

This paper concerns certain \(L\)-functions. The author studies the values of \(L(\pi \otimes \chi,0)\), where \(\pi\) is a cuspidal automorphic representation of \(\text{GL}_n(\mathbb{A}_{\mathbb{Q}})\) with non-vanishing cohomology and \(\chi\) is a character which is critical for \(\pi\). The author proves the rationality of values of \(L(\pi \otimes \chi,0)\), under a certain non-vanishing assumption, based on considerations of cohomology via automorphic forms and Eisenstein series.