Letter to a potential PhD supervisor (mathematics)
I am a mathematician in the UK.  If someone doing a Master's degree in Germany wants to do a PhD with me, I would like them to send me an email of five or six lines, giving a brief indication of what is in their Master's thesis, and a very broad indication of what they would like to do in their PhD (perhaps "chromatic homotopy theory" or "something to do with operads").

I do not expect that applicants will have read any of my papers, although that sometimes happens.  If your supervisor suggested that you should apply to me, then I might find that interesting, but it would not be significant; I would wait for more detailed comments in the supervisor's reference letter.