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

TL;DR

This paper establishes a connection between non-critical special values of p-adic L-functions for imaginary quadratic fields and p-adic Eisenstein-Kronecker series, specifically when conductors are divisible by p, advancing understanding of p-adic number theory.

Contribution

It introduces a novel relation between p-adic L-values and Eisenstein-Kronecker series for conductors divisible by p in imaginary quadratic fields.

Findings

Established a link between p-adic L-values and Eisenstein-Kronecker series.

Extended the theory to conductors divisible by p.

Provided new tools for studying p-adic L-functions in quadratic fields.

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 $p$.