Is it acceptable to have a research paper with no references?
Though I don't think there's any hard rule against having a paper with no reference, it seems pretty weird. Note that references are not only for citing other people's results (theorems, algorithms, etc.) which you have used, but more broadly to recognize other's scientific contribution. For example:
- Has the problem never been discussed before? Who first realized it was a problem, stated it, formalized it?
- You probably put the problem into the broader context of your field. And if you don't, you probably should. This sure requires citations on recent work on related problems, even if nothing was ever done on the one problem you're addressing.
- For example, is your problem a specific case of another problem, or does it have generalization?
- What are the consequences of your results/findings? They probably have some impact on other related problems, or practical consequences on real-life issues.
- Didn't you or your co-authors ever do any prior work on this issue?
Finally, let's see it another way: you have solved a problem, that no one else has solved, worked on, or more generally discussed. And you did so using only elementary techniques, which have been known for so long that they do not require citation. Stated like that, it may sound like either you're a genius opening an entire field of mathematics, or you're working on a useless problem that nobody cares about. You probably don't want the reviewer to be thinking that way!
I know of exactly one published paper in my field with no references whatsoever.
- Mark H. Overmars and Emo Welzl. The complexity of cutting paper. Proc. [1st] Symposium on Computational Geometry, 316–321, 1985.
The "References" section reads, in its entirety:
No references on this topic seem to exist and no useful results could be found.
No, it's not acceptable to have a paper with no references. One of the first things a referee looks for is whether the paper shows proper awareness of the current state of the art in the field and references previous, recent work properly.
What is actually somewhat more commonly encountered (although not in any decent journal) than a paper with no references is a paper in which none of the references are appropriate. For example, anti-relativity kooks will self-publish papers in which all the references are to papers from the 1920's, textbooks, their own work, and the work of fellow kooks.
In fact, one of the quickest ways of detecting that a paper is a kook paper and not worth spending much time reading is if it has these characteristics. The fact that the professors you're working with are unable to place your work in the context of current work in the field suggests very strongly that they are not competent, and this is reinforced by your description of them as being unfamiliar with publishing. You probably want to stop working with them in order to avoid embarrassment.
Becoming associated with someone who's a kook or publishes incompetent work could be the kiss of death to any future academic career you might have been hoping for.