Estimates on Eisenstein distributions for reciprocals of p-adic   L-functions: the case of irregular primes
  We consider the p-adic distributions derived from Eisenstein series in [GMPS], whose Mellin transforms are reciprocals of the Kubota-Leopoldt p-adic L-function. These distributions were shown there to be measures when p is regular. They fail to be measures when p is irregular; in this paper we give quantitative estimates that describe their behavior more precisely. 
Stephen Gelbart, Ralph Greenberg, Stephen D. Miller, and Freydoon   Shahidi
math.NT