This question is very simple.
Would someone be so nice as to send me an electronic copy of M. M. Vishik, Non-Archimedean measures connected with Dirichlet series, Mat. Sb. (N.S.), 1976, Volume 99(141), Number 2, 248–260?
This is the English translation of the Math Sbornik article in which Vishik constructs $p$-adic $L$-function for finite slope, non-critical eigencsupforms. My e-mail is accessible from my profile.