p-ADIC L-FUNCTIONS FOR UNITARY GROUPS. (6th May 2020) - EISCHEN, ELLEN; HARRIS, MICHAEL; LI, JIANSHU; SKINNER, CHRISTOPHER
Abstract : This paper completes the construction of p -adic L -functions for unitary groups. More precisely, in Harris, Li and Skinner [' p -adic L -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 p -adic L -functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and p -adic differential operators [Eischen, 'A p -adic Eisenstein measure for unitary groups', J. Reine Angew. Math. 699 (2015), 111–142; ' p -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 [STIX]x1D701 -integrals occurring in the Euler product (including at p ). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.