Hoping that my question is appropriate for MO, I would like to ask the following question: I have sent one of the editors of a very good math journal a paper of mine which contains a main result, call it theorem A. The editor wrote me that he sent my paper to referee and will contact me when he will get the referee's report (this was 7 weeks ago). A week ago I have noticed that my Theorem A can be generalized to Theorem B, and Theorem B has a nice application, which Theorem A does not have.

What should I do:

(1) Should I be patient and wait for the referee's report, and only after receiving it decide what to do with my Theorem B?

(2) Should I inform the editor about my Theorem B and let him decide whether to send it to the referee or not? On the one hand, I do not want to disturb the editor (and referee), but on the other hand, perhaps the referee will be glad to see my Theorem B? (if he is not sure if my Theorem A is good enough to be published in their very good math journal, but Theorem B is).

This question is slightly similar, but it asks about fixing an error, not about generalizing a result.

Thank you very much!

Edit: I have just found this question, which is quite similar to mine, though there are differences between the two.

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    $\begingroup$ Is theorem B and it’s application not enough for a separate paper? $\endgroup$ – David Hill Oct 3 '18 at 4:20
  • $\begingroup$ Good question. (Assuming that my results contain no errors and are nice as I think), hopefully, Theorem B and its application are enough for a separate paper. Truly, I do not mind to have two separate papers (first one with Theorem A, and a second with Theorem B+ its application). If I would have sent my paper with Theorem A to a lower level journal (call it Y) than the one I have sent it to (call it X), then perhaps things would have been easier, since perhaps it would have been reasonable to have the Theorem A result in journal Y and afterwards Theorem B+ its application in journal X. $\endgroup$ – user237522 Oct 3 '18 at 11:03
  • $\begingroup$ But since I have already sent the Theorem A paper to journal X, I feel that maybe it is not fair to not let them know that I now have a better result. Also, perhaps the referees will notice that it is possible to generalize Theorem A to Theorem B, so isn't it better to inform them about my Theorem B+ its application? I really do not know if the referees will be glad or annoyed if I will inform them about my Theorem B. $\endgroup$ – user237522 Oct 3 '18 at 11:08
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    $\begingroup$ To me the fact that it is 7 weeks ago means it is unlikely the referee has gotten far into it if at all and so it is probably ok to do (2) and advise the editor so that they can advise the referee to wait ASAP. If the paper has been around a long time it is not fair to the referee to do a big rewrite before the report. In that case I would wait for the report unless there is a way to simply add Thm B and the application as an additional chapter or appendix without changing what the referee spent time on. $\endgroup$ – Benjamin Steinberg Oct 3 '18 at 13:37
  • $\begingroup$ Good question, I am not sure about what is the best thing but (2) seems good. What happend in the end? $\endgroup$ – Jérémy Blanc Nov 26 '19 at 21:15

I myself would do (2). It adds information, enhances interest and acceptability, and is basic openness. The goal here is to enlighten and advance our understanding of the subject matter. Good luck! You should probably also prepare a careful revision for the referee's consideration.

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  • $\begingroup$ Thank you very much! Hopefully, I will decide soon. I wonder if someone will advice me to choose (1). $\endgroup$ – user237522 Oct 3 '18 at 2:41
  • $\begingroup$ I also vote for (2) — in fact I have been in this situation a few months ago (replace "very good journal" by "good"). Everything went smoothly. $\endgroup$ – abx Oct 3 '18 at 4:26
  • $\begingroup$ @abx, thank you for your comment. Nice to hear that everything went smoothly. $\endgroup$ – user237522 Oct 3 '18 at 11:15

Theorem B is the result of additional work of yours after submission of your paper of A. I would consider writing a follow-up paper later about that work. The additional advantage is that it adds a publication in your name. If my paper A as submitted would be refused, then I would write a paper A+B and submit it, probably to another journal. But anyway, before trying to add additional work B in paper A I would thoroughly check the journal's guidelines for submission to see whether that would fit or not.

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  • $\begingroup$ Thank you very much. Nice answer. BTW, I still have not decided what to do... $\endgroup$ – user237522 Oct 3 '18 at 15:53

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