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We construct $p$-adic measures which interpolate the special values ofreciprocals of $p$-adic $L$-functions of totally real number fields $K$ atnegative integers. These measures are defined by analyzing the non-constantterm of partial Eisenstein series of the Hilbert modular group of $K$.

$p$-adic Measures for Reciprocals of $L$-functions of Totally Real Fields