P-ADIC L-FUNCTIONS for UNITARY GROUPS

This paper completes the construction of -adic -functions for unitary groups. More precisely, in Harris, Li and Skinner ['-adic -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure', Doc. Math.Extra Vol. (2006), 393-464 (electronic)], three of the authors proposed an approach to constructing such -adic -functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and -adic differential operators [Eischen, 'A -adic Eisenstein measure for unitary groups', J. Reine Angew. Math.699 (2015), 111-142; '-adic differential operators on automorphic forms on unitary groups', Ann. Inst. Fourier (Grenoble)62(1) (2012), 177-243], Part II of the present paper provides the calculations of local -integrals occurring in the Euler product (including at). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.