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We can define in two different ways an L-function $L(\\rho \\times \\pi,s)$: first we can use the Langlands parametrization at each places which is now available, thanks to Arthur's work, and secondly we can transfer $\\pi$ to a general linear group, using the twisted endoscopy as established by Arthur. In this paper, we compare the two definitions and we prove, as expected, that the first one has less poles that the second one. 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