In a face-to-face meeting with a professor, he told me he would send me some papers to read. It's been almost a week, so I assume he's forgotten. That is understandable, since he has a lot to do. I would like to send an email to remind him, but am having difficulty writing it. How can I phrase it nicely?
Dear Professor X,
during our meeting last week, you mentioned that you wanted to send me links to a couple of papers. Would you mind?
I often find students agonizing over the exact wording of totally normal emails. The text above took me 10 seconds to write, and that's the amount of time you can expect the typical professor to spend on the typical email. You're not going to be held to a much higher standard either. Be polite, formal, and above all brief. Address the person at the top, sign off at the bottom. That's all that's being asked for.
In addition to the other answers, remember that most professors and other established researchers are extremely busy and overcommitted. Email often then serves as a durable marker of a task to be done, and can be seen when the person is in a position to carry out immediately (i.e., in front of their computer).
I thus often actually ask students to email me to ask for something that I've promised them, without waiting to see whether I remember on my own. That is because getting that email helps me to make sure that I actually respond promptly. In fact, my collaborators and I often do it with each other too for the same reasons, and it's surprisingly helpful.
In short: relax, and don't worry about the phrasing too much, as long as you're not actively rude.
A simple polite email will be just fine. You can write something like the following:
Dear Professor Smith,
I very much enjoyed our conversation last Tuesday. Thank you for meeting with me. In that conversation, you mentioned two papers that I am eager to read, one on post-colonial algebras and another on dialectical topology. Could you please send me the references for those articles?
Professors are busy people and it's not unusual for them to forget such things. It is perfectly fine to send them a reminder. Make sure you set some context, in case he has forgotten the discussion you had with him. Also, clearly mention what he had promised to send you. Keep it short, simple, and polite. Some of the templates above work fine.