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

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