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I have several small corrections to apply to a paper which is currently under review. The errors are - as far as I can say - not very significant. There is a citation which it would be good to include, but maybe is not crucial (I only recently discovered a paper which deals with a somewhat related problem), plus a number of typos that I recently discovered.

What is the correct way to proceed? Should I update the paper and send the corrected version to the publisher, or would it be better to wait for the referee reports and apply these corrections together with the ones the referees request? Or have I lost my chance to correct the paper when I sent it for publication, and have to accept that I can't apply the corrections I want?

There is a similar question where the accepted suggestion is to send in the corrections; however that is a significantly more serious correction than in my case. My field is mathematics, if this matters.

Edit: This question is very similar to this question with the slight difference that there they consider an error in a paper and worry about a possible rejection, and here I'm mostly concerned about modifying a paper in a way that (in my opinion) makes it better but not necessarily more correct.

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As you indicated, usually a paper is accepted with some suggestions - that is, the referee has a list of suggestions/errors. The author then addresses those suggestions/errors, and sends the edited manuscript back to the journal with a list of changes. This version is the one that officially gets accepted (I guess it's possible to go through multiple rounds of this, but I've never heard of this occurring in practice).

Since the errors/omissions you found are minor, I would just wait to hear back from the referee, since they don't truly affect your paper in any significant way, and in fact the referee might find most of them. (If your paper is on the arxiv, you might consider updating it there).

For what it's worth, you'll get the opportunity to correct typos even after the refereeing process; there is usually some editing for typos from the journal's side, and you'll also get a chance to make small changes to proofs before publication.

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    Agreed, if it's under review then you will have an opportunity to correct later when it comes back. Even after you make the corrections as suggested by reviewers, prior to publication (if accepted) you should get a pre-publication copy from publisher to review prior to print. So there is at least one opportunity to make corrections after the review process. – A.S Apr 29 '15 at 12:42

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