A Note on Lipshitz's Lemma 3

TL;DR

This paper comments on a potential flaw in the proof of Lemma 3 in Lipshitz's work on D-Finite power series, highlighting a specific questionable statement.

Contribution

It provides a critical remark on the proof of a key lemma in Lipshitz's paper, questioning its correctness.

Findings

Identifies a possibly incorrect statement in Lipshitz's proof.

Raises concerns about the validity of Lemma 3.

Stimulates further scrutiny of the proof's details.

Abstract

In this note, we give a remark on the proof of Lemma 3 in Lipshitz's paper "The diagonal of a D-Finite power series is D-Finite". This remark is motivated by the observation that the statement from line -8 to -3 on page 375 of that paper seems not completely correct.