I rarely find modern research papers (on mathematics) that are less than 5 pages long. However, recently I came across a couple of mathematical research papers from the 1960/1970's that were very short (only 2-4 pages long). The authors of both papers solved very specific problems, and stopped writing (I guess) as soon as they were done. This made me realize that I very much like short papers! When possible, I will strive to do the same with my own future papers.
Sometimes one finds short papers that are entitled "A note on...". Since I am first of all not a native English speaker and also only a junior mathematician, I would like to know what you think about my questions/thoughts:
1) Is it a good (or bad?) idea to try to let the title of the paper reflect the fact that it is short? Are there any standard ways of doing this?
2) A paper which is entitled "A note on...", is it expected to be short? How short? Can a 50-pages long paper be "A note on..." or would that not be customary?
3) At least to me "A note on..." could give the impression that the paper is a survey article where no new material is presented, but I guess this need not be the case. When is it appropriate to entitle a paper "A note on..."?
4) When is it appropriate to entitle a paper "On the ..."?