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Published online by Cambridge University Press: 02 May 2003
Let $M$ be a pure motive over $\Bbb Q$ of weight $w=w(M)$ and of the global conductor $c(M)$. Also given Dirichlet character $\chi$ one can define the twisted motive $M_\chi$; let $L(M_\chi,s)\, (s=\sigma+i t)$ denote the corresponding $L$-function.