Geodesic
Values of Twisted Tensor L-functions of Automorphic Forms Over Imaginary Quadratic Fields
Canadian journal of mathematics, Tome 66 (2014) no. 5, pp. 1078-1109

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DOI

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.
DOI : 10.4153/CJM-2013-047-5
Mots-clés : 11F67, 11F37, twisted tensor L-function, cuspform, hypergeometric series 
Lanphier, Dominic; Skogman, Howard; Ochiai, Hiroyuki. Values of Twisted Tensor L-functions of Automorphic Forms Over Imaginary Quadratic Fields. Canadian journal of mathematics, Tome 66 (2014) no. 5, pp. 1078-1109. doi: 10.4153/CJM-2013-047-5
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     author = {Lanphier, Dominic and Skogman, Howard and Ochiai, Hiroyuki},
     title = {Values of {Twisted} {Tensor} {L-functions} of {Automorphic} {Forms} {Over} {Imaginary} {Quadratic} {Fields}},
     journal = {Canadian journal of mathematics},
     pages = {1078--1109},
     year = {2014},
     volume = {66},
     number = {5},
     doi = {10.4153/CJM-2013-047-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-047-5/}
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