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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.