Forum of Mathematics, Pi ( IF 3.857 ) Pub Date : 2020-05-06 , DOI: 10.1017/fmp.2020.4
ELLEN EISCHEN; MICHAEL HARRIS; JIANSHU LI; CHRISTOPHER SKINNER

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.

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