How should one present research done in a CV to a graduate program in mathematics? This is a question about how to best convey research done to an admissions committee for graduate school.

I have basically two combating philosophies, both may be wrong:


state the "official name" of a paper that is either in preparation, published, or on the arXiv. Follow this with collaborators and perhaps the year you worked on the project.
State the field " Number Theory," state collaborators, and give a brief description of what we accomplished: "We classified classically integral quadratic forms that fail to represent at most two positive integers." Then give where the article was published and its name.


I guess for communication purposes, I like the latter, but I've never seen this done. That being said, I also have some research that is niche enough that the title will not be well-understood by a general audience of mathematicians.

Secondly, I don't like the first since it creates an asymmetry if I want to mention that I am currently doing research on my CV. I guess I can expand on my research experiences in a personal statement, but I figured that a brief description here is helpful.

I guess I want to convey the type of research I've done, since it is a bit diverse (not that much, but pretty broad) so I just wanted to know if there is a good way to proceed.

I think that option (1) is more professional, but also not helpful as it might as well say "I did X number of research projects, and this is their status."
There are some general ideas about what is "standard" to include in CVs, but they only go so far: you still have some leeway on what to include and how to include it.  

It is fine to give a brief description (e.g. the abstract) of your works on your CV.  You should certainly also include all of your collaborators!  Either way, you should take some space in your "personal statement" (a bit of a misnomer -- it should be a "professional statement," not e.g. a narrative about how you came to love mathematics) to describe this work.  

Finally, for what it's worth -- I was familiar with your paper on quadratic forms, and I just looked back at it again.  I wouldn't quite describe it as "analytic number theory."  It has some analytic number theory, some computational number theory and some, well, quadratic form theory (that's on the algebraic side of number theory but I wouldn't quite describe it as "algebraic number theory").