p-adic Eisenstein-Kronecker series and non-critical values of p-adic Hecke L-functions of an Imaginary Quadratic Field when the conductor is divisible by p

Abstract

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series, when the conductors of the algebraic Hecke characters are divisible by $p$.