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We propose a definition of thep-adic L-function of a motiveM over ℚ assumingM admits at least one critical point, andp is ordinary forM. This corrects by a power of$$i = \sqrt { - 1} $$ an earlier definition of B. Perrin-Riou and the author.

On $p$-adic $L$-functions Attached to Motives over $Q$