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We consider the p-adic distributions derived from Eisenstein series in[GMPS], whose Mellin transforms are reciprocals of the Kubota-Leopoldt p-adicL-function. These distributions were shown there to be measures when p isregular. They fail to be measures when p is irregular; in this paper we givequantitative estimates that describe their behavior more precisely.

Estimates on Eisenstein distributions for reciprocals of p-adic L-functions: the case of irregular primes