p-Adic automorphic L-functions on GL(3)

摘要

We construct -adic -functions attached to cohomological cuspidal automorphic representations of over . These functions will be defined as -adic Mellin transforms of -admissible measures. Our strategy is to generalize the construction of -adic -functions given in Mahnkopf (Compos. Math. 124(3):253-304, 2000) for cuspidal representations of which are cohomological with respect to the trivial coefficient system. This mainly relies on Harder's method of computing bounds for the denominators of certain Eisenstein cohomology classes, cf. Harder (Kohomologie Arithmetischer Gruppen, 1987). Finally, we establish a functional equation for the -adic -functions. This, in particular, requires the construction of -adic -functions attached to the critical integers on the right-hand side of the functional equation.