How to approach experts to get feedback on a paper

I'm a PhD student in pure maths at a university in Europe. For reasons that I won't go into, my research interests do not coincide with my supervisor's ones. This means that, although she gives me good general advice, she can't give me more "technical" feedback on my work. I've now written a complete first draft of my first paper, and I'd like to get some external feedback before thinking of submitting it to a journal. My question is:

What is the best way to approach the experts in my field (for whom I am a complete stranger) to politely ask if they can read my paper and give some feedback on it?

Emailing, of course, would be the preferred means of communication, so suggestions on how to structure a potential email to send to the experts are very welcomed.