$p$-ADIC $L$-FUNCTIONS FOR UNITARY GROUPS. (6th May 2020) - EISCHEN, ELLEN
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 $\unicode[STIX]{x1D701}$ -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.