I asked a similar question before, (Mentioning Professors in math PhD applications) but I want to ask specifically about emailing professors I want to work with.
I want to do a math PhD, and unfortunately I don't know enough about research level math to make a comment about a professors' research papers. The most I can say is that I am interested in the field. How would I phrase my email? Here is a draft:
"Dear Prof. X,
I am a student in at University A and I am applying to University B this fall. I was wondering if you are taking any prospective students next year. I am interested in topic Y (which is what Prof X is working in), and I would also like to ask for some good references to study topic Y."
How would this email sound? Of course, I would add more details about what courses I've taken and prerequisite knowledge that I have. But is this a good email? Are there other questions/comments I should add?