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Search: MSC category 11F37 ( Forms of half-integer weight; nonholomorphic modular forms )

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Lanphier, Dominic; Skogman, Howard
Values of Twisted Tensor $L$-functions of Automorphic Forms Over Imaginary 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 $GL_2(\mathbb{A}_K)$, 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.

Keywords:twisted tensor $L$-function, cuspform, hypergeometric series
Categories:11F67, 11F37

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