#### DOCUMENTA MATHEMATICA,
Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 393-464

** Michael Harris, Jian-Shu Li, Christopher M. Skinner **
p-Adic L-Functions for Unitary Shimura Varieties
I: Construction of the Eisenstein Measure

We construct the Eisenstein measure in several variables on a quasi-split
unitary group, as a first step towards the construction of p-adic L-functions
of families of ordinary holomorphic modular forms on unitary groups. The
construction is a direct generalization of Katz' construction of p-adic
L-functions for CM fields, and is based on the theory of p-adic modular
forms on unitary Shimura varieties developed by Hida, and on the explicit
calculation of non-degenerate Fourier coefficients of Eisenstein series.

2000 Mathematics Subject Classification: Primary 11F33, 11R23; Secondary 14G35

Keywords and Phrases:

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