  The integral model of a GU(n-1,1) Shimura variety carries a universal abelian
scheme over it, and the dual top exterior power of its Lie algebra carries a
natural hermitian metric. We express the arithmetic volume of this metrized
line bundle, defined as an iterated self-intersection in the Gillet-Soule
arithmetic Chow ring, in terms of logarithmic derivatives of Dirichlet
L-functions. We also determine the arithmetic volumes of Kudla-Rapoport
divisors and relate them to coefficients of Eisenstein series.
