Some factorization results for formal power series
Abstract
In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for formal power series. The information about prime factorization of the constant term up to a unit and that of some higher order terms is utilized for the purpose. Further, using theory of Newton polygons for power series, we extend the classical Dumas irreducibility criterion to formal power series over discrete valuation domains, which in particular, yields several irreducibility criteria.
Cite
@article{arxiv.2501.05375,
title = {Some factorization results for formal power series},
author = {Rishu Garg and Jitender Singh},
journal= {arXiv preprint arXiv:2501.05375},
year = {2026}
}
Comments
13 pages. The second updated version is rewritten in more general setting (e.g. formal power series over PIDs and over Discrete valuation domains) where as previous version the study was restricted to $\mathbb{Z}[[z]]$. Title and abstract are alightly changed