Requesting endorsement for arxiv from future professor as a high-school graduate I finished high-school, and would like to publish articles on arxiv. I got into university, and found out that a professor of the institue of mathematics is submitting papers to the site. I start my first semester next month, and do not know him, however I would like to publish an article this week.

Is it a good idea to ask for endorsement from him? If so, what is the “best” way to ask?

I would like to do research in the future too, as I am extremely interested in the subject (analysis) and I have been learning it for a long time.
This sounds to me like a great opportunity to introduce yourself and possibly find a mentor relationship in the bargain.  

Just be succinct and straight-forward about who you are and what led you to contact this particular professor.  I would also recommend taking the opportunity to invite the professor to give you feedback, which 1) may be sorely needed and 2) might be the beginning finding some interesting research connections as an undergraduate.

An email you write might go something like this:


  Hello, Professor Ridcully:
  
  You don't know me yet, but I'm going to be a student at Unseen University this Fall, and I am interested in mathematical research.  I've already been working some on my own, and have put together a manuscript that I would like to post on arXiv.  I'm contacting you because I need somebody to endorse my submission, and noticed that you have recently posted on arXiv as well.  If you would be interested in giving me feedback on this work, I would be interested in that as well.
  
  Please let me know if you are willing to help, and I will send you my manuscript.