This is a question that has been in my mind for a long time. Now I am a M.Sc. first year student in mathematics and planning to apply for graduate school next year in Europe. But for applying to graduate schools, it is written that first I have to write an email to a supervisor along with a idea of a research project and I have to convince him that I am well prepared to work under him as a PhD student. Also, it is recommended that you should study the papers of professors to whom you are applying.
Now, I am interested in a topic. My college does not offer that topic. So, I have learned the topics on my own. Also, at this moment I do not participate in an internship program because of this pandemic situation all over the world. That is why I have decided that I will read some papers of the professor to convince him that I am well prepared to work under him.
My question is as follows: How do I demonstrate that I read and understood a professor's paper to the professor?
Please advise me. Thanking in advance.