# Tauberian theorems for $k$--summability with respect to an analytic germ

## TL;DR

This paper develops tauberian theorems for $k$-summability in multiple complex variables, extending one-variable results through monomialization techniques to analyze summability with respect to analytic germs.

## Contribution

It introduces a framework for tauberian theorems for $k$-summability in several variables based on monomialization of analytic germs, expanding the scope of summability theory.

## Key findings

- Established tauberian theorems for $k$-summability in several variables.
- Extended one-variable tauberian results to multivariable settings.
- Utilized monomialization methods to analyze analytic germs.

## Abstract

The goal of this article is to establish tauberian theorems for the $k$--summability processes defined by germs of analytic functions in several complex variables. The proofs are based on the tauberian theorems for $k$--summability in one variable and in monomials, and a method of monomialization of germs of analytic functions.