Values of Twisted Tensor L-functions of Automorphic Forms Over Imaginary Quadratic Fields

Let $K$ be a complex quadratic extension of $\mathbb{Q}$ and let ${{\mathbb{A}}_{K}}$ denote the adeles of $K$ . We find special values at all of the critical points of twisted tensor $L$ -functions attached to cohomological cuspforms on $G{{L}_{2}}\left( {{\mathbb{A}}_{K}} \right)$ and establish Galois equivariance of the values. To investigate the values, we determine the archimedean factors of a class of integral representations of these $L$ -functions, thus proving a conjecture due to Ghate. We also investigate analytic properties of these $L$ -functions, such as their functional equations.