I'm a student. A professor recently gave me an open question to think about, and after three months of working on it as a hobby, I think I have something good.
It is not an exact mathematical theorem or anything, but I have the code and some proofs in special cases. So, I'm writing a paper and thinking about publishing it.
Now, the professor isn't active in the research area that this paper would naturally fit in. They did help with the technical details, but have no time to become an expert in this area.
But, all papers in this area have an "Introduction" section of almost a page, citing 30+ papers from the past two years. I have read a grand total of four relevant papers.
How to proceed? I don't think I am capable of doing this in a reasonable amount of time, as I don't really follow what's going on in this research area. And I have other pressing things to do.
I am thinking about writing to some PhD students in my institution which publish in this area, to recruit them as coauthors. Maybe they could even improve the paper. But how to contact them? Is it dumb to say: "hi, nice to meet you, here is my current draft of the paper, do you want in? By the way, you are going to write first section"?