I submitted an article in a Reputed journal in mathematics. It is in review process. After 4 months, i realized that there are some trivial mistakes... Article is still under review with journal. What should I do?
I am feeling very bad because of me editor and reviewer are (will be) wasting their time with wrong article...
You should do both. Namely, send an email to the editor, explain the error and how you fixed it, and attach a revised version, and ask them how they would like to proceed. They might
In any event, you must contact them.
I think it depends to some extent on the magnitude of the error, and the complexity of the correction.
If you have found a serious error in one of the results, and the correction involves major changes to the proof, or requires a significantly stronger hypothesis or weaker conclusion, then I agree with the other answers that you should contact the editor and ask that the corrected version be sent to the referee (include a list of the changes you made). Otherwise the referee may waste a lot of time sorting it out, or just reject the paper.
If you have found some typographical errors, or a stray factor of 2 in a constant, or omitted an obvious hypothesis in a lemma, then I would not bother the editor and referee with it. Minor errors like this should not affect the acceptance of the paper; the referee should have no trouble realizing what you meant (or may overlook it completely). If the paper is accepted, you can include the correction with any other revisions requested by the referee (as before, include a list of all changes). If the paper is rejected, it wouldn't be because of these errors, and you can simply fix them before submitting to a new journal.
You'll have to decide where your corrections fall between these two.
Do not worry about this situation. It happens to best of us. The best strategy is to write a note explaining the mistakes and the modifications you have made to correct them. Then send the note and the revised version to the editor.
Please note that it is very important to list all the modifications of the revised version.
First of all, when you send a Journal to review, is not a trivial matter, and you must be sure all the math is correct, that is the reason you are supposed to have it checked by colleagues and people who can give you thoughtful insight, it would come as unprofessional to an editor if suddenly an author says: "sorry I made a mistake, lets do it all over again"
In the best case scenario, the mistakes will be so trivial that the reviewers will realize it and accept it given that you correct the mistakes.
In the worst case scenario, is because of these mistakes that the journal would get rejected.
You can always try and resubmit, put I would try a different journal.
