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I recently posted my two-page paper to arxiv and sent it to the editor of a good journal. The editor responded:

"Your result is not substantial enough" and so it was rejected."

I cannot say that I totally disagree with the editor, the paper does not make any significant progress on number theory but I can't say that my paper is totally without value. It is the first time I have tried to publish a paper, and I am confused:

  • Was my paper rejected because it is too short?
  • Should I submit it to another journal?

I would really appreciate if someone gave me some advice on how to proceed.

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    Perhaps you should discuss this with your advisor. – user102 Dec 17 '13 at 11:48
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    The formula from wikipedia seems to be sufficient to get your result. What you do is asymptotics, because you just say that some function is closer that 1/2 from another function infinitely often. Now tell me how that is not asymptotics. Sorry, just try to ask people at Math.SE for a proof of your theorem, I believe that you'll get one in 10 minutes (unless people consider it completely non-interesting). If everything posted there was worth publishing, we would all be screwed. – yo' Dec 17 '13 at 12:35
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    (1) "Substantial" does not mean "Long". A short paper can make a substantial contribution if it gives deep insight. A long paper can make an negligible contribution if it says nothing new. (2) The general advice to publishing is "edit and try again". But the editing usually should reflect the comments from the editors and the referees in the letter of rejection. When the charge is that the result is not substantial enough, you either (a) agree, in which case you find a journal whose bar for publishing results has lower threshold for "substantial" or (b) disagree, in which case you edit... – Willie Wong Dec 17 '13 at 12:59
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    ... the manuscript to include a discussion of why your result is substantial. (Literature review and comparison to other current works are heavily encouraged.) – Willie Wong Dec 17 '13 at 13:00
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    Evaluating individual research papers isn't really on topic here, but here's a little information. I like your formula, but unfortunately I don't think it's really novel or important enough to be published in a good journal. There many journals out there, and it could certainly be published somewhere, but you probably wouldn't be happy with some of the papers that would be published alongside it. Posting it on the arXiv means it will be archived and can already be cited. Beyond that, you could publish it in a journal, but I don't see a strong scholarly or career argument for doing so. – Anonymous Mathematician Dec 17 '13 at 13:38
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I am no expert in number theory, so I can't really help you with the last question (if you should submit your paper to another journal). However, it sounds like the editor stated the reason for rejection pretty clear: In his impression the results are not substantial enough. This is a valid (and frequent) reason for rejection. So in this respect you are in good company. If the editor did not state explicitly that he finds the paper "too short" than there is no reason to believe that this was the reason for rejection.

To get good feedback on how to proceed with your paper and your research you should ask your advisor (or find one).

  • i do not have any more an advisor i have graduated in 2010 and for some serious reasons i was out of research since then. I sent an e-mail to one of the proffesors that i used to have good connection but he replied "my mother is in the hospital we will talk again after some days" etc (this happened before 6 months)I sen him the paper and told him to answer whenever he could (but he did not) – Konstantinos Gaitanas Dec 17 '13 at 11:56

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