$p$-adic $L$-functions for $P$-ordinary Hida families on unitary groupsIn this paper, we construct a $p$-adic $L$-function for a $P$-ordinary Hida family of cuspidal automorphic representations on a unitary group. We first describe the geometry and representation theory involved in the study of such $P$-ordinary automorphic representations. Then, we construct a $p$-adic family of Siegel Eisenstein series and use the doubling method of Garrett and Piatetski--Shapiro-Rallis to relate certain zeta integrals to special values of standard $L$-functions. The $p$-adic interpolation of these special values is obtained by looking at the $p$-adic variation of the Fourier coefficients of the Siegel Eisenstein series.
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