Geodesic
$p$-ADIC $L$-FUNCTIONS FOR UNITARY GROUPS
Forum of Mathematics, Pi, Tome 8 (2020)

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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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ELLEN EISCHEN; MICHAEL HARRIS; JIANSHU LI; CHRISTOPHER SKINNER. $p$-ADIC $L$-FUNCTIONS FOR UNITARY GROUPS. Forum of Mathematics, Pi, Tome 8 (2020). doi: 10.1017/fmp.2020.4

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